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MSU Is An Affirmative Action/Equal Opportunity Institution

A STUDY OF STATISTICAL EQUILIBRIUM IN A NUCLEAR SYSTEM

AT LOW BOMBARDING ENERGIES

BY

Jeong Ho Lee

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1988

ABSTRACT

A STUDY OF STATISTICAL EQUILIBRIUM IN A NUCLEAR SYSTEM

AT LOW BOMBARDING ENERGIES

BY

Jeong Ho Lee

We have studied a reaction of ”Ar + 12C at EI/A=8, 10, and 12 MeV.
Fragments ranging from the lithium isotopes to the titaniums were
detected at small forward angles (9211“). Gamma-rays in coincidence
with these fragments were also observed. The analysis of source
velocities and simultaneous events suggests a characterization of
complex fragment emission as a binary-decay process of the compound
nucleus. In order to investigate whether the composite system formed
from the projectile and the target ever reaches statistical equilibrium,
the new temperature measurement proposed by Morrissey et a1. has been
applied to complex fragments including fragments of A>1O for the first
time. Temperatures of 2-3 MeV, which roughly agree with those from the
Fermi gas model under the assumption of thermal equilibrium, were
obtained from the 7L1, “’Be, and ”B at E/A=8 and 10 MeV, however
temperatures from the fragments of A>1O show a fluctuation from nucleus

to nucleus and also from transition to transition in the same nucleus.

In addition to this, temperatures for most fragments at E/A=12 MeV are

lower than those at the lower beam energies. This discrepancy was taken

as to be due to the effect of the preferential feeding from the higher—A
nuclear unbound states rather than the non-equilibrium effects at this
beam energy. For the heavy residual fragments, the observed relative

populations of nuclear states are compared with those predicted by the

CASCADE statistical model. The result suggests that heavy fragments

with masses close to the total mass in the reaction are produced from
the compound nucleus by the statistical emission of light particles,

such as nucleons and alpha-particles. However, the relative populations

of nuclear states for fragments of Z<2O show discrepancies between the

observations and the predictions of the statistical model.

To my mother

iv

ACKNOWLEDGMENTS

To my advisor, Dr. Walt Benenson, I owe my deepest gratitude for
raj; guidance, encouragement, and supervision during my graduate career.
As a civil engineer and a field—army artillery officer, I had never
thought that the transformation to a nuclear physicist would even be
possible. However, he made me believe that it was possible» euui
encouraged me to work hard and finally to finish this work. His
patience, depth of vision, sense of humor, and understanding have been
greatly appreciated and are acknowledged.

My special thanks go to Dr. David Morrissey fkn~lais continuous
advice and comments on the work. His help, guidance, and deep knowledge
of this field have made the completion of this work possible. In
addition, I must thank Dr. Mitsuru Tohyama for his advice and numerous
discussions, and Dr. Tetsuya Murakami for his instructions and fuuiitful
discussions about the CASCADE model. There are also many more co-
workers and contributors who I must mention for thanks; Drs. R. Blue, C.
Bloch, E. Kashy, 0. McHarris, and R. Ronningen, and also Y.M. Chen, K.
Hanold, M.F. Mohar, and H.M. Xu.

Finally, I must offer special and sincere thanks to Mr. and Mrs.
Imsuk Yang. Their interest in me and their care for me during tn“; last
four years have been just like family love to me. I also love their
kids, Yuree and Sungsang. There are many more names in my hear%:, and I

thank all of you - "Yuruboon, gamsahamnidah!"

LIST OF

LIST OF

Chapter

I

II

III

IV

TABLE OF CONTENTS

Page
TABLES .................................................... Viii
FIGURES ................................................... x
Introduction .............................................. 1
I 1 Motivation ......................................... 1
1.2 Introduction ....................................... 2
Experimental .............................................. 11
11.1 Experimental Set-up ................................ 11
11.2 Electronics ....................... ' ................. 1“
11.3 Calibration ........................................ 17
11.“ 8Be Contamination in the 7Li Singles Spectra ....... 22
Particle Singles .......................................... 27
111.1 Data Analysis ...................................... 27
111.2 Particle Singles Spectra ........................... 35
111.3 Slope Parameters ................................... 62
111.4 Fermi Gas Model .................................... 68
Population Distribution 1 (Complex Fragments) ............ 71

vi

IV.1 Introduction ........................

IV.2 Data Analysis .......................
IV.3 Light Fragments .....................
IV.“ Intermediate Fragments ..............
1V.5 Errors ...............................

V Population Distribution 11 (Heavy Residual

v.1 Introduction ........................

V.2 Statistical Model ...................

v.3 Population of Nuclear States ........

V1 Summary and Conclusions ....................
LIST OF REFERENCES .................................

vii

............... 71
............... 7A
............... 75
............... 87

............... 121

Fragments) ..... 12A

............... 13A

............... 165

............... 173

TABLE

11.“.1

III.1.1

III.3.1

111.“.1

1V.3.1

1V.A.1

LIST OF TABLES

Page
Evaluation of contamination of the 8Be ground state in
the 7Li singles spectra ................................. 26
Detection of fragments.
3) Energy ranges (units in MeV) .......................... 34
b) Predicted kinetic energies and energy losses at
E/A:1O MeV, Glab=11° (units in MeV) ...................... 3“
Kinetic energy spectra fitting parameters
for complex fragments .................................... 66
Nuclear temperatures in the Fermi Gas model
(units in MeV) ........................................... 67
Deduced nuclear temperatures from 7L1, 7Be, and '°B ...... 83
Deduced temperatures from intermediate fragments.
a) At E/A:8 MeV .......................................... 111
b) At E/A=1O MeV ......................................... 112
c) At E/A=12 MeV ......................................... 113
Input parameters for CASCADE calculation ................. 130
Relative intensities of gamma-rays at E/A:8 MeV.
a) For “5T1 .............................................. 152
b) For HTi .............................................. 152
Relative intensities of gamma-rays at E/A=8 MeV.
a) For ““80 .............................................. 153
b) For “58c .............................................. 153
Relative intensities of gamma-rays at E/Az8 MeV.
a) For “’Ca .............................................. 15A
b) For HCa .............................................. 155
Relative intensities of gamma-rays at E/A:8 MeV.
a) For “°K ............................................... 156
b) For “‘K. .............................................. 157
c) For “’K ............................................... 158
Relative intensities of gamma-rays at E/A:8 MeV.
a) For "Ar .............................................. 159
b) For ”Ar .............................................. 159

viii

V.3.6

V.3.7

Relative intensities of gamma-rays at E/A:8 MeV.

a) For "Cl .............................................. 160
b) For 37Cl .............................................. 160
Relative intensities of gamma-rays at E/A:8 MeV.

a) For ’38 ............................................... 161
b) For “S ............................................... 161

ix

FIGURE

II.1.1

11.2.1

11.3.1

II.3.2

III.1.1

III.1.2

III.1.3

III.2.1

III.2.2

III.2.3

III.2.A

III.2.5

111.2.6

LIST OF FIGURES

Page
Experimental set-up of detectors.
a) Outside (NaI-detectors) ............................... 15
b) Inside (Si-telescopes and Ge—counters) ................ 15
Electronics Schematic .................................... 16
Schematic of Si-element calibration ...................... 2O
Time—of-flight spectrum for gamma-rays in the NaI(Tl)
detector at 9:20° in coincidence with ‘°B fragments in
any telescopes, E/A:12 MeV ............................... 21
A1E+A2E vs E light fragment PID spectrum (Tel-2) ......... 29

A,E+A2E vs E intermediate fragment PID spectrum (Tel-2).. 3O

A,E vs AZE PID spectra (Tel-A).

a) At E/Az8 MeV .......................................... 31
b) At E/A:1O MeV ......................................... 32
c) At E/A=12 MeV ......................................... 33
Particle inclusive kinetic energy spectra (3§Z§11).

a) At E/A=8 MeV..... .................. .. ................. 39
b) At E/A=1O MeV... ...................................... A0
0) At E/Az12 MeV ......................................... A1
Particle inclusive kinetic energy spectra (2212).

a) At E/A=8 MeV..... ............... . ..................... A2
b) At E/A=1O MeV ......................................... A3
c) At E/Az12 MeV ......................................... AA
Velocity Diagrams.

a) At E/A=8 MeV .......................................... A5
b) At E/A:1O MeV ......................................... A6
c) At E/A:12 MeV ......................................... A7

Differences between the peak energies and the calculated
Coulomb barriers in the center-of-mass frame ............. A8

Median velocities of the forward-scattering and the
backward-scattering peaks for complex fragments .......... A9

Simultaneous events for 2,:7 between telescope-2 and

X

III.2.7

III.2.8

III.3.1

IV.3.1

IV.3.2

IV.3.3

IV.A.1

IV.A.2

telescope-3 (solid line) or telescope-A (dotted line)....

21 - Z2 correlation plot for simultaneous events between
telescope-2 and telescope-3. Arrow drawn indicates
the total charge (Ztot) of the system.

a) At E/A=8 MeV ..........................................
b) At E/A:1O MeV .........................................
c) At E/A:12 MeV .........................................

The Lorentz-invariant differential cross sections for
heavy residual fragments.

a) At E/A=8 MeV ..........................................
b) At E/A=1O MeV .........................................

Slope parameters for complex fragments. Lines are drawn

for the eye-guide ........................................

Doppler-shift corrected Y-ray energy spectra (NaI)
in coincidence with light fragments.

a) At E/A:8 MeV ..........................................
b) At E/A:1O MeV .........................................
c) At E/A=12 MeV .........................................

Y-fractions. Dashed line represents the predicted
Y-fractions with the Fermi gas model temperatures.
Decay schemes are from Refs. Aj8A and A185.

a) For 1Li ......... . .....................................
b) For 7Be ...............................................
c) For ‘“B ...............................................

The observed temperatures from the Y—ray transitions in

the light fragments. See the text for the lines .........

Doppler-shift corrected Y-ray energy spectra (NaI)
in coincidence with intermediate fragments.

a) With “N ..............................................
b) With "O ..............................................
c) With ‘°O ............................. ' .................
d) With "F ..............................................
e) With 2°Ne .............................................
f) With 2‘Ne .............................................
g) With 22Ne .............................................
h) With Z’Na .............................................

Y-fractions. Lines are the predicted Y-fractions with
the Fermi gas model temperatures. Decay schemes are
from Refs. AJ83 and A386.

a) For “N ...............................................
b) For 1"0 ...............................................
c) For "O.. .......................................... ...
d) For "F ...............................................
e) For z°Ne ..............................................
f) For "Ne ..............................................
g) For 2"’Ne ..............................................

53

5A
55
56

6O
61

65

76
77
78

79
80
81

82

88
89
90
91
92

9A
95

IV.A.3

IV.A.A

IV.A.5

IV.5.1

V.2.1

V.3.3
V.3.A
V.3.5
V.3.6
V.3.7

VI.1.1

h) For 23Na ..............................................

The observed temperatures from the Y—ray transitions of
the intermediate fragments. Dashed line represents the
predicted temperature in the Fermi gas model.

a) At E/A:8 MeV ..........................................
b) At E/A:1O MeV.... .....................................
c) At E/A:12 MeV .........................................

Y—fractions after the preferential feedings from heavier
nuclei (dashed lines). The data points and the solid
lines are same as in Figures IV.3.2 and IV.A.2.

a) For light fragments ...................................
b) For intermediate fragments ............................

Cross sections for complex fragments. Solid lines
represent the predicted cross sections by the quantum
statistical model [St83, Fi86] ...................... .....

An example of the Y—ray peak fittings for 2°Ne. See
the text for detail ......................................

Predicted primary population density distribution by the
CASCADE code [P877]. See the text for detail.

a) For “’Ca ..............................................
b) For 3aAr ..............................................

Doppler-shift corrected Y-ray energy spectra (Ge)
in coincidence with Titanium (Ti) ........................

Same as in Figure V.3.1 with Scandium (Sc) ...............
Same as in Figure V.3.1 with Calcium (Ca) ................
Same as in Figure V.3.1 with Potassium (K) ...............
Same as in Figure V.3.1 with Argon (Ar) ..................
Same as in Figure V.3.1 with Chlorine (Cl) ...............
Same as in Figure V.3.1 with Sulfur (S) ............. .....
Doppler-shift corrected Y-ray energy spectra (NaI)

in coincidence with Potassium (K).

a) At E/A=8 MeV. .........................................
b) At E/A=1O MeV .........................................
c) At E/A=12 MeV ........................ . ........... .....
Summary for the temperature measurements in the complex
fragment region. See Figures IV.3.3 and IV.A.3(a-c) for
detail....... ...... .. ......... ..... ..... . ................

103

108
109
110

117
118

119

123

132
133
1A2
1A3
1AA
1A5
1A6
1A7
1A8

1A9
150
151

172

CHAPTER I: INTRODUCTION
1.1 Motivation

One of the main goals of intermediate energy heavy-ion physics is
to create and study nuclear matter at high temperature and density. In
order for this goal to be achieved, it must first be demonstrated that
thermodynamic quantities, like temperature and density, are applicable
and then that they are in fact measurable in nuclear reactitnus in this
energy range. A key question, therefore, is whether thermal equilibrium
is ever achieved in any part of the system. Another one is, if a hot—
equilibrated system is produced in a reaction, how it decays into a
cooler system.

In order to study the above questions a new method for temperature
determination and study of population distribution was proposed by
Morrissey and collaborators [M08Aa, Mo85a, M086a]. This method was
inspired by temperature measurements of stellar surfaces and is
essentially a measurement of the production of complex fragments in
excited states. In order to test whether the method is in fact
applicable to nuclear systems, an experiment [Mo86a] was devised for a
low energy compound nuclear system in which thermal equilibrium has been
shown to exist, and for which the temperature is known from the Fermi
gas model. The results at E/A=8 MeV were consistent with thermal

equilibrium at the calculated temperature but included a large

I-1

1-2
correction for the rotational energy of the system, which had to be
calculated with a model [M086a]. In addition the results of this
experiment were limited to a light compound system which emitted light
fragments [M086a].

This thesis describes a more definitive test of the population
method for temperature determination by the utilization of a heavier
compound nucleus for which the rotational energy is a much smaller
contribution. In addition, the use of reverse kinematics permitted the
study of excited heavy complex fragments and also heavy residual
fragments for the first time. The energy range covered ranges over the
region in which there is a transition from the very well understood
compound nucleus into the incomplete-fusion regime, which is much more

complex and less well understood.

1.2 Introduction

In low energy heavy-ion collisions, from the neighborhood of the
Coulomb barrier up to bombarding energies of E/A=7-8 MeV, complete
fusion (full-momentum transfer or formation of the compound nucleus) is
a dominant process in the entrance channel. When the projectile energy
increases but remains below a few tens of MeV/nucleon, the dominance of
the complete-fusion process slowly fades out as the competition between
complete and incomplete fusion (incomplete-momentum transfer or deep-
inelastic scattering) becomes important. Thus, a multi-dimensional
space in the entrance channel which includes the relative velocity
[M08Ab, Ch83, He83, V182] and distance [Ba7A] between two colliding

nuclei, the mass asymetry [Hi87, St85, Mo8Ab, Ch83, R083, V179, Ba7A],

1-3
and angular momentum [H187, Mo86b, 8186, M185, Hu83, V182, St77, Br76,
Ba7A, Co7A, Kn60] is needed to characterize these processes.

The decay mode of the composite system formed through complete
fusion or incomplete fusion has been well characterized in this
relatively low energy regime. Emission of nuclei with masses of four or
less (especially emission of protons, neutrons, and alpha-particles) at;
low beam energy is generally considered to arise from nuclear
evaporation after energy thermalization. As the energy increases over
the point at which incomplete fusion starts competing with complete
fusion in the entrance channel, one can observe in addition light
particles that evidently are emitted at an early stage of the reaction,
prior to the formation of the composite system. This is known as pre-
compound or pre-equilibrium product and is generally considered to be a
forward-peaked high energy component [Mo85b].

Heavy residual fragment emission, which is connected to very light
particle emission, is well characterized as the formation of evaporation
residues and as the main decay mode of the compound nucleus with mass
lighter than A=HM3 [Mo8Ab] in low energy reactions. For the higher
projectile energies one must deal with the competition between the
evaporation and the fission in the decay of the compound system because
of the dramatic lowering of the fission barrier with increasing angular
momentum [C07A, PI7A]. The production of evaporation residues at higher
energies, therefore, is limited by angular-momentum-dependent fission
competition. Incomplete fusion will commonly take place in a wide range
of linear momentum transfers, hence the array of final states is
expected to be doubly complicated by the combination of the entrance and

exit channel effects. Since the two different processes for forming the

I-A

composite system, complete fusion and incomplete fusion, are often
indistinguishable from each other, some difficulties in experimentally
defining the complete fusion process for heavy residual fragment
emission arise as the beam energy increases. The general difficulties
in the measurement of evaporation residue velocities to determine the
average linear momentum transfer to the composite system and in the
measurement of the angular correlations between the emitted complex
fragments (or fragments with masses intermediated between the alpha-
particle and the symmetric-fission products) to provide the information
about the possible fission mechanism have been nicely avoided by
employing a reverse-kinematics reaction [Ch87a, H187, M086b, M185,
M08Ab, SoBA] and by characterizing the emission of complex fragments as
a binary-decay process of the composite system [Ch86a, M085, 8083].

Symmetric fission reactions which follow fusion processes and
produce fragments close to one-half the mass of the composite system are
traditionally observed in heavy systems. In light systems (A g 100), in
which the fissility parameter is smaller than the so-called Businaro-
Gallone limit [Bu55], the distribution of fission products will be
governed mainly by the mass, charge, and angular momentum of‘tflua
composite system. The dependence on the fissility parameter and the
role of the Businaro-Gallone point have been studied in Refs. Gr8A and
808A. Different results from the two references may beixmtuned to
propose that below the Businaro-Gallone point the expected yields
monotonically decrease toward symmetry, while at larger angular momenta,
which lowers the Businaro—Gallone limit below the fissility parameter, a
peak in the yield is expected at symmetry. This indicates that in

higher energy reactions, within the critical angular momentum, the yield

1-5

at symmetry will become larger than at lower energy [M087, M088]. One
can also notice that production of the heavy complex fragments
(especially close to the symmetric-fission products) via an incomplete-
msion process is less likely than that via a complete-fusion process
because the pre-equilibrium light particles, in general, carry away a
great amount of the orbital angular momentum in the entrance channel.
Hence, the composite system has a much lower fraction of the angular
momentum and a lower excitation energy than the completely fused system
[Mo86b, M185]. The angular momentum effect on the distribution of the
fission products can be associated, in a somewhat different manner, with
a statistical emission theory developed by Moretto [M075]. A model
introduced in Ref. M075 predicts that complex fragments with masses
between alpha-particles and symmetric fission fragments must be emitted,
although with lower probability compared to the yields of the heavy
residual fragments and the very light particles, by decay of the
compound nucleus. The standard evaporation formalism and the fission
decay formalism are nicely combined in this model to describe the
transition from the very light-particle emission to the emission of a
very sizable fragment of the mass of symmetric-fission products. Hence
the light complex fragments (but still Z>2) can be produced by both the
evaporation and the fission process of the compound nucleus.

On the other hand, composite systems are often characterized as
thermally equilibrated hot zones with a temperature (usually called
"kinetic" temperature) which is obtained by fitting simple Maxwell-
Boltzmann distributions to particle singles inclusive spectra. The
concept of an equilibrated zone of nuclear matter has been also extended

to the relativistic heavy-ion collisions by introduction of the

1-6

"fireball" model [We76, (3078]. Evidence of the existence of a common
moving source has been presented in a measurement of intermediate-
rapidity light fragments in the intermediate energy range [Ja83, (H3831.
This broadly extended theory of the formation of a thermalized hot zone
combined with the characterization of compound—nucleus emission of
complex fragments [Ch86a, Mc85, 8083] in the heavyanMIreactions has
been widely accepted in studies of statistical equilibrium of the
nuclear system at various energies. One of the most relevant methods to
obtain information concerning the statistical behavior of‘tflne nuclear
rmatter, therefore, is to measure the particle singles inclusive spectra
for the light fragments, which may be emitted at longer time evmxhition,
hence giving information about space-time extent, velocity, and energy
involvement of the highly excited nuclear systems (or moving sources).
The moving source fit [We82, Ja83] has been commonly used for reactions
at various energies [c.g. Ch86b, F186, P085, F18A, We8A], sun: evidence
for more than one moving source, such as target-like slow moving source,
intermediate-rapidity moving source, or projectile-like fast moving
source, has been obtained as well. The temperatures deduced from this
nmving source fit generally exhibit a systematic dependency on
bombarding energy, as expected, but not on the fragment mass.

A recently introduced nuclear temperature measurement by Morrissey
et al. [M08Aa, Mo85a] has given another insight into the reaction
mechanism. Initflns new technique, it is suggested that nuclear
temperature also can be characterized by the relative population of
bound states of light complex fragments (Li, Be) in nuclear reactions.
The observed populations of the excited states at intermediate energy

reactions, however, show that the deduced temperatures are significantly

1—7

lower than those obtained from the kinetic energy distributions of the
fragments. This similar discrepancy has been shown by other authors
[P085, Xu86, Ch87c], some of whom have extended this technique to the
measurements of population of the particle unbound states in similar
fragments [P085, Ch87c]. This surprising result may imply that
equilibrium is never achieved in this energy range. More complicated,
but not unambiguous, explanations for this discrepancy have been
presented; for example, preferential feedings to certain states from the
particle unbound states in the higher-A nuclei [M085a, Mo8Aa, St83,
Ha87, Ha88] and final state interactions among the expanding nuclei and
nucleons [808A]. However, the corrections on these possible effects are
not well known experimentally.

Morrissey et al. [Mo86a] has discussed the new temperature
measurement more widely by the introduction of the average thermal
temperature, which was calculated from the Fermi gas model and compared
to the results obtained from reactions over a wider energy range (6.25
MeV < E/A < 25 MeV). Over this energy range, the major entrance channel
process changes dramatically from complete fusion to incomplete fusion
as the energy increases [Go8A, St77]. In this measurement, populations
of nuclear states are found to be distributed according to the average
thermal temperature, which is described in Ref. Mo86b, at bombarding
energies up to around E/A=8 MeV. However the population distributions
appear to be much lower than the calculated values at energies of E/A=12
MeV and higher. The agreement of the two temperatures (the observed and
the calculated) below E/A=8 MeV implies the formation of an equilibrated
system. However, a correction for the fraction of the average

rotational energy to the total excitation energy in a nuclear reaction

1-8
must be made since it plays an important role in populating the light
fragments. The latter can be studied further by comparing two different
reactions, heavier and lighter systems, at similar energies, while the
question on how the "kinetic" temperature is related with the population
distribution of light fragments [Ch87c] remains as a complicated problem
which is yet to be solved.

In this thesis we report the results of measurements for the
reaction ”Ar + ”C at E/Az8, 10, and 12 MeV. The present experiment
was performed as a continuation of a study of the thermal population of
nuclear states reported in Ref. M086a. A heavier system (relative to
that in Ref. M086a) was employed in the present experiment to study the
importance of the rotational energy fraction on the nuclear temperature.
Reactions at E/A=8, 10, 12 MeV may show very rapid changes in reaction
mechanism at early stages of the collision, and studies of the light
particle emission can provide valuable information concerning
statistical equilibrium. Inclusion of the measurement at E/A=1O MeV was
necessary in order to complement the large difference in the
characteristic of the relative populations of the excited states between
E/A=8 and 12 MeV, which is presented in Ref. M086a. The use of reverse
kinematics avoids, in general, the detection of projectile-like light
fragments and direct-reaction products. This may be compared to the
normal kinematics, in which there exists the favored detection of fast-
moving quasi-elastic or inelastic scattering light fragments. In
addition, reverse kinematics permitted the detection of a large number
of complex fragments as well as the heavy residual fragments in the
present experiment. The detection of the heavy residual fragments and

the clear identification of these fragments by charge for this reaction

1-9
provided some advantages in studying the fusion process in this energy
range. Gama-rays in coincidence with fragments ranging from lithiums
to titaniums were detected at all the projectile energies. The
detection of gamma-rays in coincidence with the individual intermediate
fragments (12$A523) was possible owing to the excellent particle

identification provided by the silicon surface barrier particle

telescopes.
Experimental details are given in Ch. 11. Particltz:singles
inclusive spectra are presented in Ch. 111. Evidence of the

statistical—binary decay of the complex fragments is given by presenting
the "peak-velocity" diagrams and results from the simultaneous events.
In Ch. IV, the results for the population distribution of nuclear states
for the complex fragments (3§Z§11) are presented. The first attempt to
apply the new nuclear temperature measurement to the much heavier
fragments (A>10) is described in this chapter. Gamma-ray intensities
measured in coincidence with heavy residual fragments are compared, for
the first time, with the statistical model calculation in Ch V.
Finally, summary and conclusions are presented in Ch. VI.

Throughout this thesis, the "light fragments" refer to the
fragments with masses between the alpha-particle and the target nucleus
(‘2C). The "intermediate fragments" represent the fragments
intermediate between the target nucleus and the projectile nucleus
(”Ar). However, for the practical reason, isotopes of Ar, Cl, and S
are referred as the "heavy residual fragments", which are defined as
fragments that may be evaporation residues from the composite system.

"Light fragments" and "intermediate fragments" are often referred as

1-10
"lighter complex fragments" and "heavier complex fragments",

respectively, or the "complex fragments" altogether.

CHAPTER II: EXPERIMENTAL

11.1 Experimental Set—up

Mass fragments ranging from 2:3 to 2:22 were produced by the
interaction of argon ions with a carbon target. Beams of 320 MeV “”Ar‘+
ions, A00 MeV “°Ar7+ ions, and A80 MeV “°Ar7+ ions were provided tn! the
K500 cyclotron of the National Superconducting Cyclotron Laboratory at
Michigan State University. The cyclotron periods were 107.558 ns,
95.93A ns, and 87.712 ns, respectively. inuetarget was a self-
supporting foil of '20, A90 ug/cm2 thick. The target was mounted irleui
aluminum target ladder inside the scattering chamber with its plane at
A5° relative to the beam. The chamber had 12 ports every 30° starting
from 0° with the same vertical level. The beam entered through the open
180° port and exited through the open 0° port. The ports at.‘HN)° and
ZNHJ° had 8.5cm x 19.5cm cylindrical aluminum cups with the center lines
centered on the target, and the end of each aluminum cup was about (Scan
away fwwnn the target (see Figure II.1.1b). The rest of the ports had
either a clear Lucite window or a Lexan plate with high-vacuum
electronic feed-throughs. An arm was located at about 2 cm above the
table inside the chamber, and both could be rotated from the outside the
chamber. The beam was stopped in a Faraday cup, which was approximately
3.2 m downstream and was surrounded by water and lead shielding. The

beam intensity was generally between 5 and 10 nA. Such a low beam

II-11

II-12

intensity maintained the count rates of the gamma-ray detectors below
20,000 per second and thereby avoided count-rate dependent gain shifts.

Charged particles (Z>2) were detected in a set of three element
silicon surface barrier telescopes each with a 50 mm2 area. The events
with 2:1 and 2:2 were rejected in a Motorola 68000 based system [Va85] .
Telescopes were located inside the chamber approximately at the
azimuthal angles of 0: 111° relative to the beam and the polar angles of
¢= 1A° [(0,¢):(—11°,-A°), (-11°,A°), (11°,—A°), and (11°,A°) for Tel-1,
2, 3, and A, respectively]. This relatively small angle with respect to
the beam line was used to optimize the count rate for the reverse
kinematics while avoiding the detection of projectile fragments or
direct reaction fragments by keeping the angles bigger than the
classical grazing angle 0:6”. Two telescopes at the same azimuthal
angle were in one aluminum mount, which had provisons for liquid
cooling. Refrigerated alcohol was run through the mounts to cool the
detectors approximately to -20°C throughout the experiment. The three
elements ( A,E-A2E-E ) of each particle telescope were 30 um, 75 um, and
1000 um thick, respectively. Approximately 0.1 mg/cm2 thick gold cover
foils were placed on the collimators of the particle telescopes to
reduce the number of electrons hitting the silicon detector. All of the
four particle telescopes were placed approximately 20.3 cm from the
target. The effective solid angle of each particle telescope was
approximately 870 usr. The particle identification of the particle
telescopes was excellent for isotopes with charges up to 2:11, however
only the Z-identification was possible for the heavier fragments (2)11).

A set of eight NaI(Tl) scintillation detectors, 7.60m x 7.60m right

cylinders, and a pair of Ge counters, A.71cm x A.36cm cylinders, were

II-13

used to detect gamma-rays in coincidence with the particth Eight
NaI(Tl) scintillation detectors are placed on the domed lid of the
scattering chamber with the azimuthal angles, 0: 120°, 160°, 1120°, and
i160°, and the same polar angle, ¢2A9°. Two Ge counters were placed at

: t120° in a horizontal plane (020°). A schematic diagram of the
experimental setup is shown in Figure 11.1.1. The Ge counters were
cooled down by liquid nitrogen to approthuxfly -196°C throughout the
experiment. The resolutions of NaI(‘1‘l) scintillation detectors were
equal to 9.A% or less at EY:57O KeV, and those of Ge counters were about
0.A5% or less at the same gamma-ray energy. This good resolution for
the germanium counters was necessary to identify the gamma-ray lines
from the heavy residual fragments and to determine accurately the number
of counts in those gamma-ray peaks. Since heavy residual fragments are
slower moving sources (<v>zO.1 c) than the complex fragments, the
Doppler Shift corrections for these fragments are relathmfly small.
Therefore, errors which arise from the D0ppler broadening due to the
finite solid angles in the gama-ray detectors will be also small. The
NaI(Tl) scintillation detectors provided sufficient statistics in the
gamma-ray energy spectra for most of the complex fragments. Even though
the relatively poor resolution for the NaI(Tl) scintillation detectors
makes it difficult to separate closely spaced gamma-ray lines, the
bigger total detecting efficiency as compared to the Ge counters (£=3.5%
at EY=A30 KeV while Ge counter had a total efficiency of 0.A5% at the
same gamma-ray energy) was essential in the detection of the gamma-rays
in coincidence with complex fragments which have much lower yields than
the heavy residual fragments. The gains of the gamma-ray amplifiers

were set to observe a maximum gamma-ray energy of about 2.2 MeV.

Il-1A

11.2 Electronics

A schematic diagram of the basic electronics for the particle
telescopes and the gamma-ray detectors is shown in the Figure 11.2.1.
ORTEC AD811 analog-to—digital convertors (ADC's) were used to digitize
the pulse heights of the signals for the silicon detectors and the
NaI(Tl) scintillation detectors, and AOOMHz ADC Model 7A20/G's were used
for the Ge counters. The time information was recorded for all the
detectors by using LeCroy 2228A time-to-digital convertors (TDC's).

A coincidence between A,E and AZE or AZE and E silicon elements was
required to get a valid particle telescope event. The valid event for
Ge counters and that for NaI(Tl) scintillation detectors were formed
separately, and at least one of the each gamma-ray detector type was
required to fire. The particle singles mode was triggered by the
particle telescopes only. The particle-gamma coincidences modes were
triggered by the simultaneous event of at least one of the four particle
telescopes and at least one of the ten gamma-ray detectors. The gamma-
gamma coincidence mode, which was employed in the efficiency calibration
of the gamma-ray detectors, was triggered by the simultaneous event of
at least one of the eight Na1(Tl) scintillation detectors and at least
one of the two Ge counters.

Selection of the mode was made between runs on a coincidence
module. When this master gate coincidences mode was "true", and the
computer signal "not busy" was present, the digitized pulse height, the
time information, the integrated beam current signal, and the timing of
the master gate against the cyclotron RF were recorded. A sealer buffer

was made at every 3 minutes throughout the entire experiment. These

II-16

.omm h_m
mkm<Hm
mmuoh

machm
w.ooh.

mwmomhm
mmuo<

mNToouamS

   

.omm :m a 53% $33 one at}.
E a a

E a Eugé lag

mmu<om oo<

Euaow a u

zm4<om

  

 

 

 

 

 

 

 

Electronics Schematic.

Figure II.2.1

11-17
buffers were sent to a Vax 11/750, and they were written to tape at 6250

bpi. Program SARA was used to sample the buffers during the experiment.

11.3 Calibration

An energy cnrlibration was obtained for each silicon detector with
pulsers and two alpha—sources (“sz and “’Cf). The linearity of the
electronics was checked with the pulsers four times during the
experiment. Extra data for the calibration were taken right after the
experiment with the gains increased by a factor of 3 for the A,E and AZE
silicon detectors, and by a factor of 5 for the E silicon detectors.
This new gain was set in order to get the alpha-lines on scale (Z‘ZPb
has alpha-particle lines of 6.051, 6.090, and 8.78A MeV, euui 2HCf has
an alpha-particle line of 5.812 MeV, all of which are very close to the
threshold set for the silicon detectors under the original gains for the
experiment). Only the 8.78A and 5.812 MeV alpha-particle lines were
used in this calibration because the 6.051 and 6.090 MeV alpha-particles
are too closely located and also had too little statistics in comparison
to those for the other two. A linear fit between the known alpha-
particle energies and the observed channel numbers determined the
calibration at the higher gains (except the A,E silicon element, the
thickness of which, 30 um, was too thin to stop 8.78A MeV alpha-
particles). Then, this calibration determined the energies for the
pulser dial's readings at the same gains, and, finally this calibration
was transformed to the original gains after a simple algebraic
manipulation. More specifically, if the pulser dial's reading (PD) is

defined as PDzAH+BH0Ch in the higher gains and PD:AL+BL-Ch in the

II-18
original gains with Ch representing the channel number, and also if the
energy in the higher gains is defined as E:A+B-Ch from the calibration
of the alpha-lines, then the energy in the original gains can be

expressed by

B BL
E = [A+-B—}-{-(AL-AH)] + BEHOCh . (11.1)

A schematic explanation for this procedure is shown in Figure 11.3.1.
The superimposed lines are from the best linear-fitting for the data.
The lowest-lying line represents the alpha-calibration. Geographically,
this line can be transformed by rotating and shifting into the middle
line which represents the pulser dial scale in terms of the channel
number. After that, it can be transformed in the same sense into the
the top line which represents the pulser dial scale at the original
gain. A calibration for A,E silicon detectors followed the same routine
except for borrowing the calibration from the AZE silicon detectors for
the lower gains. This calibration was checked by generating a two-
dimensional particle identification spectrum (A,E+A2E vs E), and the
particle separation in the spectrum was much clearer than that obtained
simply by using the linear fit between the reading of the pulser dial
and the observed pulse height. Two-dimensional particle identification
spectra for the light fragments, the intermediate fragments, and the
heavy residual fragments will be shown in Ch. 111 (Figures from III.1.1
to III.1.3C).

The energy calibration of the NaI(Tl) scintillation detectors and

the Ge counters was performed several times throughout the experiment

11-19
with gamma-ray sources. The Ge counters had very consistent
calibrations, whereas the NaI(Tl) scintillation detectors had some drift
problems, but the changes were within the resolutions of the detectors
except the NaI(Tl) scintillation detector at 0: -120°, which was
excluded from the analysis.

The detection efficiency calibrations of the Ge counters were
obtained with a ””Eu gamma-ray source (standard reference material
A218-C, National Bureau of Standard). The efficiency calibrations of
the NaI(Tl) scintillation detectors were obtained with a gamma-gamma
coincidence method using gamma-ray sources: ”Co, 1“Cs, and 2""81.
These gamma-ray sources have two prominent gamma lines with one
following the other as a sequence. A gamma-ray singles mode run for the
Ge counters was carried out for each gamma-ray source, and the excellent
resolution of the Ge counter provided two sharp gamma-ray peaks for each
source in the gamma-ray energy spectrum. Then, a gate was put in the
preceding game-ray peak in the Ge-counter gamma-ray energy spectrum,
and the sequential gamma-ray was observed in the NaI(Tl) scintillation
detectors in the gamma-gamma coincidence mode. Multiple chance events
of the preceding gamma-rays were subtracted from the sequential gama-
ray counts according to the assumed efficiency conversion factor and was
iterated after the resulting efficiency calibration. Angular
distribution effects were negligible after summing the efficiencies to
get the total efficiency for the Na1(Tl) scintillation detectors. A
reverse way of the coincidence calibration, by putting a gate in the
sequential gamma-ray peak and observing the preceding gamma—rays, was
also performed in order to check the efficiency calibration. These

three gamma-ray sources gave the efficiencies for the ganma-ray energy

II-20

 

I’ ‘l’ r I I I l I I I I l I I I I

* 0 Original Gain
200 I. X 5 d 200

~ 0 X 5 (on—Lines)

 

 

 

150 — - 150 m
i * ‘ z
--' to
Q :0
D: 100 — - 100 Q
a . . “<1
.4 4— E
D . (D
04 50 f <’—/ 50 5
IIIII-le' C J
0 - 0
b l a l . J . . . . l . . . i l . . . .
0 1000 2000 3000 4000
CHANNEL

Figure 11.3.1 Schematic of Si-element calibration.

II-21

 

1000 :_ E/A=12 MeV_E

...s

O

O
I
l

 

COUNTS / ns
23

 

AJILI

 

 
   

 

 

 

 

 

150 200 250 300 350

l

1
1

 

TOF (ns)

Figure 11.3.2 Time-of-flight spectrum for gamma-rays in the NaI(Tl)
detector at 9:20° in coincidence with ”B fragments in any telescopes,
E/A:12 MeV.

11—22
above 570 KeV. A gamma-ray singles run with the Na1(Tl) scintillation
detectors was performed later on with a ‘°°mHo multi-gamma—ray source
to provide the shape of the efficiency curve for EY<570 KeV region, and
the two curves were joined smoothly to give the efficiencies for the
entire gamma-ray energy region.

The TDC's were calibrated by comparing the periodicity of the time-
of-flight (TOF) histogram to the period of the cyclotron. Figure 11.3.2
shows a TOF histogram for gamma-rays in the NaI(Tl) scintillation
detector at the angle (0:20°, ¢:A9°) in coincidence with ”’8 fragments
for E/A=12 MeV. The ratio of a real-to-random coincidence was
approximately 18:1 at this beam energy (typically it was about 35:1 at
E/A:8 MeV and 25:1 at E/A:10 MeV). The average number of channels
between the prominent peaks for each TDC was set equal to the cyclotron
period, and this determined the TDC calibration, which was 0.25

ns/channel in the 2“ channel scale.

11.A aBe Contamination in the 7Li Singles Spectra

It is well known that particle singles spectra of 7L1 are
contaminated by the production of the ground state of °Be and its
subsequent a-a decay [Wo72, 8186]. The Q-value of the “Be ground state
decaying into a pair of alpha particles is 92 Kev, which is very low
compared to half the typical total kinetic energy of 100 MeV, provides a
very low relative kinetic energy between alpha particles. This
indicates that there exists a very high probability for both a's from
the 'Be fragment to be detected simultaneously in a particle telescope.

As discussed in Ref. 8186, when two a's pass through a silicon element,

II-23
they will lose the kinetic energy in a very similar way to that of a
’Li, hence contaminating all the 7Li singles inclusive kinetic energy
spectra.

The evaluation of the contaminant fraction required a theoretical
estimate of the 8Be yield because of the lack of experimental data
needed to employ the method suggested in Ref. 8186. A statistical
method was employed for this calculation. In a chemically equilibrated
composite system, the population of nuclear states in the decay products
is assumed to be relevant to the Boltzmann distribution with the
excitation energy and the spin of the state and the chemical potential
[To88, H387]. Therefore the total cross section of a nucleus produced

from this system can be written as

B.E.+Ei-uZZ-uNN
0 a Z (2ji+1) e “T , (11.2)
1

 

where ji and E1 are the spin and excitation energy of the state i, B.E.

is the binding energy of the ground state of the nucleus, and ”N are

”2
the chemical potentials for proton and neutron, respectively, 2 and N
represent the numbers of protons and neutrons, respectively, and KT is
the temperature of the system. The summation in i is over the states
that decay into the ground state of the same nucleus. In comparison
with the assumption that the fragment distributions depend mainly on the
ground state properties of the emitted nuclei [So8A, M085], the
characteristic structures [Ha88, H387, Fi8A, St83] are taken into

account in Eq. 1V.7 to formulate an expression of the relative

population for a nuclear system. However feedings to the bound states

lI-2A
from the particle unbound states in the high-A nuclear system [Ha88,
Ha87, F187, Mo85a, Mo8Aa, St83], which will be discussed in Ch. IV, are
not taken into consideration in this calculation.

Since the chemical potential and the temperature are the only
unknown parameters in Eq. 11.2, one needs only two cross sections or
more to solve this equation if one is to deal in a same type of
isotopes. We used the three cross sections of ’Be, 9Be, and ‘°Be which
are obtained in the present experiment. The result of the best fit is
given in Table 11.A.1. The temperatures of 2.6 MeV at E/A:8 MeV and 3.2
MeV at E/A:10 MeV are consistent with those from the Fermi gas model
[shown in Ch. 111], while the chemical potentials slightly differ from
each other. Finally a Monte Carlo simulation [8186] was carried out to
evaluate the probability of two alpha particles from the ground state of
“Be entering the particle telescope simultaneously. The shape of the
kinetic energy spectra of t"Be was borrowed from that of 9Be to consider
the effect of the the punch-through problems in the ”’Li spectra on the
evaluation of the contamination. The estimated contamination of the 8Be
on the 'Li spectra were 10% at E/A:8 MeV and A% at E/A:10 MeV. The
ratios of the cross sections at E/A:12 MeV were not available because of
the punch-through problems of the fast moving fragments. Nevertheless
the estimated value at E/A:12 MeV was roughly about 1%, and this was
statistically negligible. The changes in the deduced temperatures were
from 1.1 MeV to 2.2 MeV at E/A:8 MeV and from 1.8 MeV to 2.A MeV at
E/A:10 MeV, however these were comparable to the statistical errors at
the both cases. This relatively small contamination (compared to 50% in
Ref. 8186 and 70-90% in Ref. M086a) was mainly due to the smaller solid

angles in the particle telescopes (we used ~0.9msr solid angle for each

11-25
telescope, while solid angles in Ref. 8186 were 5-22msr and those in

Ref. M0863 were approximately 2Amsr).

11-26

Table II.A.1 Evaluation of contamination of the 8Be ground state in the

7Li singles spectra.

 

738 108
M 31%] 111—982]
(MeV)
8 0.25 0.28
10 0.36 0.36

 

(MeV)

2.6
3.2

8Be
_U__ R(9B€]
(MeV)

 

Contamination

 

-8.65 2.A 10%
-8.95 1.A A1

 

CHAPTER III: PARTICLE SINGLES

111.1 Data Analysis

The three-element silicon particle telescope provided a number of
options for observing the yield in the different mass regions; (1) light
fragments (2(6), which include Li, Be, and B, (2) intermediate
fragments, which refer to isotopes of C, N, 0, F, Ne, and Na in this
paper, (3) heavy fragments, which include isotopes of Mg, Al, Si, P, S,
Cl, Ar, K, Ca, Sc, and Ti. Although some of heavy fragments are lighter
than the projectile nucleus ”Ar, this classification was chosen for
convenience. The term "complex fragments" refers to both the light
fragments and the intermediate fragments.

We obtained excellent particle identification for the individual
light and intermediate fragments with charges 2:3 to 2:11 by generating
two dimensional particle identification spectra. Isotope separation by
2 only was obtained for fragments with 2>11, which leaves the
identification within a given element unresolved for this heavy mass

region. A spectrum of A,E+A,E vs. E T for the light fragments is shown

T0
in Figure III.1.1, and that for the intermediate fragments is shown in
FIBUPe III.1.2. Figures III.1.3(a-c) show two-dimensional spectra of
A13 Vs. AZE at E/A:8, 10, and 12 MeV, respectively. Unfortunately, the

2‘separation of the heavy residual fragments is poorly displayed in

these figures .

III—27

III-28

Even though a relatively large range of masses was observed with
good identification, 3 number of problems arose from the limited energy
range allowed by the gains in the silicon elements and also ffiwnn their
thicknesses. First, the total thickness of 1105um in the three silicon
element telescope was enough to stop the relatively fast moving light
fragments, such as lithium and beryllhunismnopes. As shown in Figure
III.1.1, punch-through problems appear for some of the light fragments,
and this limited the statistics for those fragments since the high
energy part was missing. Secondly, the energy range in the AzE-detector
was too low to detect majority of the slow-moving intermediate fragments
and most of the fast-moving heavy residual fragments. The energy range:
:hi the A,E-detector was set to cover the entire mass range. Meanwhile,
the mathmienergy range set in the AzE-detector was far below that
required to utilize most of the intermediate and heavy residual
fragments detected in the present experiment, as shown in Table III.1.1.
The energy ranges of each silicon element for the particle telescopes
are given in the part a) of the table. Part b) of Table 111.‘|.1 shows
the calculated energy losses in each silicon element for the predicted
peak-velocity energies for both backward-scattering euui forward-
scattering fragments (in the center-of-mass frame) at E/A:1O MeV. As
predicted from the calculation, the saturation of signals in AZE
amplifier for the fast-moving heavy residual fragments (especially for
2>12) are seen in Figures III.1.3(a-c). 'This means that tine recorded
kinetic energies of those fragments<k>rmn;represent the real energies
lost in the detectors. The peak velocity of the backward-scattering
fragments in the center-of-mass frame was not expected to be observed

for most of the fragments because of the threshold set in the detectors.

III-29

 

 

 

 

 

240 —
A
(ll
.4.) 200 —
orfi
Cl
:3 160 -
"E
(D 120 —
‘~—a’
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<1
+
m 40 —
.vd
<1 . . _
O l l I I J l
0 4O 80 120 160 200 240

ETOT (MeV)

Figure III.1.1 A,E+A2E vs E light fragment PID spectrum (Tel-2).

III-30

 

N
4;
C)

N
(3
CD

03
CD

 

CD
CD

A1E+A2E (arb. units)

 

 

 

ETOT (MeV)

Figure III.1.2 A,E+A,E vs E intermediate fragment PID spectrum (Tel-2).

III-31

 

..-. .¢-_~.-..-.~‘4‘I-.. -,..;..-...,.>._.-_~. ~ g...” urn-14.343152,“ g."--o‘~ ..-...-v~.~.‘I.-...-.,-....~'
. l . , .

    

        
  

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’ ‘_\ “-'L—,‘ 15.‘ , l

fifin;é&¢xféfig§3kp

Ru‘r
an.”

AIE (arb. units)

 

AZE (arb. units)

Figure III.1.3 A,E vs AZE PID spectra (Tel-A). a) At E/A=8 MeV.

 

III-32

 

 

 

 

 

AZE (arb. units)

Figure III.1.3 (cont'd.) b) At E/A:10 MeV.

III-33

 

 

      

    

. .. .. . ... .3

. yr»

.W,uww .fl?

1rd .
m?

   

_M.

4
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..
x
.«fl

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1
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240 —j

200 a“

Amfin:

16C)

150 200 240
AZE (arb. units)

120

8C)

  

:12 MeV.

c) At E/A

Figure III.1.3 (cont'd.)

III-3A

Table III.1.1 Detection of fragments. 3) Energy ranges (units in MeV).

 

 

Telescope No. 94E gig E
1, 2, and 3 195 100 260
A 195 183 260

 

Table III.1.1 (cont'd.) b) Predicted kinetic energy and energy ltnss at

E/A210 MeV, 0 :11° (units in MeV).

lab

 

 

 

 

 

 

 

 

Backward Scattering Forward Scattering
Isotope <KE> Energy Loss <KE> Energy Loss

ALE AAE‘ E Total Alg ALE E Total
7Li 5 5 0 0 5 107 2 A 8A 90
7Be 3 3 0 0 3 120 3 7 109 120
‘°B 8 8 0 0 8 152 A 12 136 152
12C 11 11 0 0 11 175 7 17 151 175
1“N 15 15 0 0 15 195 10 25 160 195
‘°O 20 20 0 O 20 213 13 35 165 213
‘9F 30 30 0 0 30 23A 17 50 167 23A
2‘Ne 38 38 0 0 38 2A7 22 65 160 2A7
23N3 A7 A7 0 0 A7 258 26 75 157 258
stg 57 57 0 0 57 266 32 97 137 266
27Al 69 69 O 0 69 272 39 125 108 272
2’Si 83 83 O 0 83 276 A7 160 69 276
"P 99 96 3 0 99 277 56 202 19 277
3"S 126 106 20 0 126 276 67 209 0 276
36C1 151 112 39 0 151 268 79 189 0 268
3"Ar 18A 115 69 0 18A 252 95 157 0 252
“‘K 1) 233 11A 119 0 233
“3C3 2A5 12A 121 0 2A5
HSc 257 133 12A 0 257
“'Ti 268 1A3 125 0 268
5°V 285 152 133 0 285

 

1) Given value for the nucleus of “‘K or heavier represents the

predicted average energy as an evaporation residue. See the text.

l'.‘

.-
1..

on

III-35

Data from the particle-singles runs with telescope-A, which had a larger
energy range in AZE, were crucial in determining the peak velocities,
and also better statistics were provided by the telescope-A for the
coincidences runs. None of the heavy residual fragments reached the
last silicon element (F) in the present reaction, and most of the useful
heavy residual fragment data are of those scattered into the back-
hemisphere, but the physics should not be altered by this.

Techniques for the optimized selection of the thicknesses and the
gain-settings in the silicon detectors could be improved in future
experiments if one is to observe the complete mass region, however one
has to deal with the resolution in the mass region of the most interest.
The higher gain-settings established in the second SIIIIKHI elenmnits in
the present experiment were necessary for the resolution of the light
fragments. (hmenay use two amplifiers per each silicon element with
different gain-settings in order to detect the entire mass region
without losing significant statistics (for instance, higher gain for

lighter fragments and lower gain for heavier fragments).

111.2 Particle Singles Spectra

Particle-identification gates were drawn for each of the nuclei or
isotopes in the different 2-dimensional spectra. Particle inclusive
kinetic energy spectra for each of'those gates were obtained for each
particle telescope from the singles runs. Figures III.2.1(a-c) show the
typical particle inclusive kinetic energy spectra of light fragments and
intermediate fragments at each beam energy, and those for heavier

fragments are shown in Figures III.2.2(aec). The superimposed solid

III-36
lines drawn in Figures 111.2.1(a-c) represent a Maxwell-Boltzmann
equation fit in the center—of-mass frame. This will be discussed in the
following section along with the slope parameters and the Coulomb
corrections. An interesting feature in the particle inclusive kinetic
energy spectra shown in the figures is the evolution of the shapes from
Maxwellian-like for the very light particles to Gaussian-like for the
heavier fragments as predicted by Moretto [M075], which supports the
theoretical work concerning a continuous transition of the decay mode
from the evaporation-dominant mass region to the fission competition
region as the fragment gets massive. The dashed lines shown in Figures

III.2.2(a-c) represent v c050 where 8 11° for all of the

CM lab’ labz
fragments. The change in the shape of the particle inclusive kinetic
energy spectra in Figures 111.2.2(a-c) from the intermediate fragments
to the heavy residual fragments is quite remarkable. One should notice
that the two peaks in the kinetic energy spectra for fragments of Mg,
Al, etc. (although many of them show only part of the peak because of
the limited energy range) represent the backward-scattering fragments
and the forward-scattering fragments in the center-of-mass frame.

Peak velocities for some selected masses at every available angle
were taken from the kinetic energy spectra to draw velocity diagrams at
each bombarding energy. These are shown in Figures III.2.3(3-c). The
calculated Coulomb barriers for "’Be, ”F, and 2"Al are drawn (in order
of decreasing radius) centered around the head of the center-of—mass
velocity vector in order to compare with the peak velocities. For the
light evaporation particles, if a Maxwell-Boltzmann distribution of

NanEe-E/KT represents the particle inclusive singles spectra in the

III-37
center-of-mass frame, then the peak velocity (or the most probable

velocity) should appear at the energy,

E' = secul + KT , (111.1)

where ECoul represents the Coulomb potential energy, and KT is the
temperature. On the other hand, the average kinetic energy of fragments
is expected to be ECOU1+2KT in the center-of-mass frame. In the
calculation of the Coulomb potential energy, a temperature cfi‘iUT:3 MeV

and the distance between two nuclei in the binary decay,

1/3 “-1/3

r : 1.2(A,- +A, ) + 2 (Fm)
was assumed. As the shape in the kinetic energy spectra evolves from
the Maxwellian-like for the very light evaporation particles to the
Gaussian-like for the massive complex fragments, it is expected that the
peak energies in the center—of—mass frame will appear at slightly higher
values tfluui that given by Eq. 111.1, or around at the average kinetic
energy (ECOU1+2KT). The differences between the peak energies and the
(malculated Coulomb barriers for the complex fragments in the center-of-
mass frame are shown in Figure III.2.A. The dashed lines represent tine
average peak energies for the data at each beam energy after subtracting
the calculated Coulomb energies. About 5 MeV is obtained from the data,
and this value is closer to 2KT than KT of the Fermi gas model
temperature for this nuclear reaction, which is about 3 MeV.

Even though the limited data for the backward—scattering fragments

made it difficult to observe the entire scattering shape of the

III-38

fragments, clear evidence can be observed in Figures III.2.3(a-c)
regarding the existence of the Coulomb velocities [Ch87a] in the moving
source frame. First of all, the decreasing radius of the peak velocity
with the increasing fragment mass (as required by the momentum
conservation) and its rough agreement with the calculated Coulomb
velocity indicate that the fragments are emitted with a velocity
determined mainly by the Coulomb repulsion energy between the two
decaying nuclei from composite system. This is strongly supported also
by the larger velocity for 7Be than that for 7L1 in the center-of-mass
frame. In addition, some of the intermediate fragments for which both
peaks were observed show that the peaks for the same 2 species at every
available angle lie roughly on a Coulomb circle centered on the origin
of the center-of—mass frame. One should note that the existence of the
Coulomb velocities for the complex fragments indicates that those
fragments were produced mainly in a binary-decay process from a
composite system which may have been formed in either complete-fusion
reactions or incomplete-fusion reactions.

Additional information concerning the characteristic of the
complex-fragments decay was obtained by determining the median velocity
between the backward-scattering peak and the forward-scattering peak.
This method may be an advantage of the usage of the kinetic energy
spectra since, for many cases, the median velocity can be determined
even when only part of the kinetic energy spectrum with a saddle shape
was observed as shown in Figures III.2.2(a-c) for some of the
intermediate fragments. The Lorentz-invariant differential cross

2
section 9;, 303v (where v is the laboratory velocity of the fragment)

 

should have a minimum value at the median velocity. Under the

III-39

120(4"Ar,X), E/A=8 MeV, 110

 

1"13 160
C a
a1" .. .
r 1 .'
E 1 ’

 

 

COUNTS PER MeV

     

D

I: .
I -'

" I-

D

. ' ’ I]
.J..l.ii.l...ll....l....l........l....l....l....l..l..l...
40 00 80 100120140 100125150175200 125150175200225

K.E. (MeV)

 

 

 

 

 

Figure III.2.1 Particle inclusive kinetic energy spectra (3525.11). 3)
At E/A:8 MeV.

III-A1

12C(40Ar,X), 153/.1212 MeV, 11°

 

 

 

COUNTS PER MeV

 

 

 

 

 

illll.ul..llli [unluulull .. ..l....l....l.l. l.
50 100 150 200 100 150 200 250 150 200 250 300

KE. (MeV)

 

Figure III.2.1 (cont'd.) c) At E/A:12 MeV.

III-A2

12C(40Ar,X), E/A-—-8 MeV, 110

COUNTS PER MeV

Figure III.2.2 Particle in

E/A=8 MeV.

 

 

 

 

 

 

t T7 1 I
; Si I ~Cl I :Ca 1
| l . l
I 1"". I *\ ’7‘
... | ' I, f _ " I
' I‘VJFK". _ :/ I I
b ’I' I ' L 1 A.
l I . - I '.
I _ I * I '
...'.I...I.I....I..-. ..I....I.I...I....I-.I....I....JI....1..
1 1 1
__I\I l _ E; l y-I( l
l l ’ I
I . ..
C I 5 E. I l 1 s | ‘
WU I f" I - :— I
' I ' |
__| l l |
E I I ' I '
...l.l.l..l....l.... .I. ..III.. I I .1....l.l.l.l. .I..
'Mgl i P I . Ar I
:7 : it : v'fl'fi ’ I
: / I .' I J~\
: 1 i 'l :0 I hf 5.. ...-x I as
I I I . |
:- I I
I I I ' — I
'.|..I.I...I....I.... ...I..g13...1....1.‘.I....I..I..I....I'..

 

 

50 100 150 200

100 150 200 250100 150 200 250

K13. (MeV)

elusive kinetic energy spectra (2212).

a) At

III-A3

12C(40Ar,X), E/A=10 MeV, 110

 

 

 

. I I I
- Si I E'Cl I FCa I
w". I- }; , - ”A
/W| E- _.' I " ~ I \
t g I E f. I .p N I
I I - f | I
> I- I I I: I, I :'_ .|.
t I l I 3 |
r III" : U
Q) I E I ,. I I I
2 I I g I I - M I '
...I....I.I..I....I ..I....I....I ...I. ...I.I....I...II....
I I 5 I
Of. A1 I {S I 5 K I
Ljil .— I : ,f’TTPTHIT P J/J~u
I I I . I . r l ‘A
0.4 ”3'“ ' F 3’ E / .
“I I I v, I ' I' I
’ IIIIIH : A, I : '1‘ I
I-l I I" ' I I. '
U] I r I .— f I
: ' E
Z I I I . #1 I
lLllLLLLlLLLLlLLLJl lllLLLllllgllllllll LLLJILLLAILIIJLLAL
D . Mg I ’ P I g‘Ar I
O '— l I W.“ t m
I- I- /
O ”(K I | .— ' | ' r "I I
. I I", ; fr I ..x' I
’ \ If t I I I I' I
_ MI] I t ' '
I t I I =— I’ I
I I ' I =/I I
I :- I ; I
...li...ll....l....l..II....I..J.I.U41 ...I....I.I...I.I...

 

 

 

 

 

100 150 200 250100 150 200 250 150 200 250 300

KB (MeV)

Figure III.2.2 (cont'd.) b) At E/A:10 MeV.

III-AA

12C(40Ar,X), E/Ale MeV, 110

 

 

 

 

 

 

 

: . I __ 7T
: Si I E—Cl I Z-Ca I
. ’/,w*"ry‘ I /gf1 I 'I
: I ' I- H
" I. I ”I I P "II
{If I I :r ,I' II J, I
> F , I E ,I' I :- II I
I I‘ I " f I : I
I E ’
2 I I ; II ~ I I
.J.I....|...,n....1 ..1..l.l.l..li...|. ......... I....I...L
L I E I
Dd .Al I PS I 5 K I
m , I,» 5 ~ I
if“ I I //I F .I’I‘I
D-I II I ’ 2" I I’ I
i {I f
I I I I I:- ," I 'I' II
CO I . '
E4 I! I I I’ I. E III I
,I I 6 I Z I" I
Z I F' i '
...li...l.i.il L IIHI..I....I.,I.I. I
D _Mg I —P I {Ar 1
C) I /L. I .x-I
. f .
I > Mal 1' I I- ’I’ I
..l' / I F -' I
I :- ,, I'
.I I I: I" | t i I
I- : I! ' ,. I
I'll I I ‘ III I f I
. I .I I I I
#0 '
I r, I g I I
I..I....I.I..I....II..I...iI.i..IlL..I. .I..I....I....II.L.

 

100 150 200 250100 150 200 250 150 200 250 300

KE. (MeV)

Figure III.2.2 (cont'd.) 0) At E/A:12 MeV.

Velocity Diagram, E/A=8 MeV

Figure III.2.3 Velocity Diagrams.

NB+

“(x +P

III-45

 

 

Target

>_I

a) At E/A:8 MeV.

‘0 l3 -+ I! '%

"LI
783
“‘3
“N
"F

+
)(
B
N
F

III-N6

10 MeV

 

 

Velocity Diagram, E/A

Figure III.2.3 (cont'd.) b) At E/A=1O MeV.

III-N7

J-> F.C.

12 MeV

A

 

ééfia

83500

 

Velocity Diagram, E/A

7Be
"’3
“N
o 1"o
”F

Target
F

Figure III.2.3 (cont'd.) c) At E/A:12 MeV.

III-48

 

 

 

 

 

a, ,
7;. E/A=12 MeV.§
=_ o _:
6%----3__3.._ ____°._-0.____°_ ..2....
A 5.:- . . ‘. 4
:33 ‘4’} " ‘. 0' 0. I] ‘E
2 3i-
v ’1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1‘
8
:3
8 6 o... 0
O .
E1] 5 ---------------- .-_'_.----.-.- ---—
| 4 .° ° .0
3
a 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
/\. '7 ‘. 13,/Il==E3 lie§VV
I31 6
O o O
V 5 _ __-_.___. ..--... ........
f.--.- O .— .
3

 

7Be 1°13 12c “N “’0 “F ”Ne
GLi “Be 1 13 13C 16N 17o 10F “Ne
“’11 “’Be 1‘0 1"N 1"o ”F ”Ne

Figure 111.2.“ Differences between the peak energies and the calculated
Coulomb barriers in the center-of—mass frame.

III-49

 

014 TI I I I III II

 

r J
.. IL IL a
0.12 -— T ‘r —

________ I.-I_.l<._*_.*._._._.-:

<1) > median

0.10

—

I

:- ------ LII-+41"?

 

 

 

0.08 — o E/A=12 MeV -
" x E/A=10 MeV :
<> E/A=8 MeV I
0.06 I 1 I I I I I I I I
6 3 1o 12 14 16

Z

Figure III.2.5 Median velocities of the forward—scattering and the
backward-scattering peaks for complex fragments.

T“

C)

E‘.

III-50
assumption of complete fusion the median velocity must be equal to
VCMcoselab’

processes with the preferential break-up of the target or the projectile

and the deviation could come from the incomplete-fusion

nucleus [MoBlIb]. The determined median velocities for the intermediate
fragments are shown in Figure III.2.5 and compared to the velocity
VCMcoselab' Masses used for the fragments with only Z-identification
(2)11 in the present experiment) were determined from the results of the
CASCADE code [P077] and the gamma-ray intensities relevant to each
nucleus with the same 2 (Ch. VI). The possible errors caused in
establishing which masses to use were checked by changing the masses by
one mass unit in either direction and combined with the experimental
uncertainties in all cases. Data at E/Azlo and 12 MeV were limited to
only a few of the isotopes, however no major deviation in the median

velocities from the predicted velocity V cosela was observed for the

CM b

entire range of beam energies, which suggests that the complex fragments
with masses intermediate between the target nucleus and the projectile
nucleus may be emitted from a moving source which coincides or nearly
coincides with the center-of—mass frame.

A reasonable number of simultaneous-multiple events, which means
events with more than two telescopes firing at the same time, was
recorded during the experiment. Those simultaneous events were mostly
between telescope-1 and A or between telescope-2 and 3. As described in
Ch. 11, this combination of telescopes defines two scattering planes
which intersect along the beam line, and each telescope lies at polar
angle 9z11° with an identical solid angle. Hence fewer simultaneous

events between telescopes in the different scattering planes (e.g.,

between telescope-1 and 3 or between telescope-2 and ii) relative to

III-51

those between telescopes in the same scattering plane can be taken as
evidence of the dominance of the binary-decay process in the exit
channel. Note that in a multi-fragmentation event, fragments may not
generally decay into the same scattering plane, and this will result in
making the chance of simultaneous events between any two telescopes
equal except between telescope-1 and 2 and between telescope-3 and II,
the planes of which are obviously too far away from the beam line. A
typical example of this is shown in Figure 111.2.6 for the case of
telescope-2 (22) with telescope-3 (2,) with 2,:7. The solid lines are
the events for telescope-2 with telescope-3 and the dotted lines
represent those for telescope-2 with telescope-4. No significant number
of events for telescope-2 with telescope-1 was obtained as expected. An
interesting tendency one can find in Figure III.2.6 is that the number
of events for telescope-2 with telescope-ll becomes comparable relative
to that with telescope-3 as 22 decreases, indicating that the fragments
with the smaller value of Z,+Z2 than the total charge in the reaction,
Z,+Z,_:21I, were formed from a composite system which was moving off the
beam line. This may be explained in two different directions; (1)
incomplete fusion is an important process in the entrance channel, which
is supported by the fact that the composite system formed from an
incomplete-fusion will not, in general, continue undeviated in the beam
direction, and, (2) the composite system is formed from a complete-
fusion reaction, and then goes through very light particle emission
(such as neutrons, protons, or alpha—particles) before emitting the
complex fragments through a binary-decay process.

The 2,-22 correlation plots of the simultaneous events between two

telescopes are shown in Figures III.2.7(a—c) for each beam energy. In

Ill—52
the analysis of the simultaneous events, a gate was put on the forward-
scattering fragments (2,) and it was found that most of the decay
partners (2,) were observed with low velocities whilfll are if] the
backward-scattering range, except the case of 2,22 (although most of the
events with Z<3 were rejected electronically during the experiment, a
large number of events with alpha—particles, which is due to the
particle-particle coincidences, was still recorded) wherein the
velocities of 22 were scattered all over the range. A dramatic change
in the velocities of the decay partners at 2.22 may imply that alpha—
particles were formed through many different channels, muflias pre-
equilibrium evaporation, deep-inelastic scattering, or consecutive
statistical emission from a compound nucleus. In Figures III.2.7(a-c)
one should note that the data scale is somewhat arbitrary ownn one 2,-
line to another because the number of forward-scattering Z,-fragments in
the telescope-3 was limited by the energy range as shown in Figures
III.1.2 and III.2.1(a—c) especially for 10§Z§12, which reduces the
number of events;n1tmus intermediate fragment region. Nevertheless,
the result shows that most of the events lie in a Z,+Z2 band which
remains approximately constant with a wider width at EI/A:12 MeV and a
narrower width at E/A:8 MeV. The average values of Z,+Z2 were roughly
estimated by considering the data only for 7§Z,§12, and those are found
to be approximately 23, 22, and 21 at E/Az8 MeV, 10 MeV, and 12 MeV,
respectively. In a fission model [R0814], the excitation energy in the
scission configuration (or presumably in the saddle-point configuration)

can be written as

E - E

* -- _ -
E ' E + Q ECoul Def Rot ’

SD CM

HEP/HERVE rWFC QENHIV‘h INF/h

III-53

400 E- i

E E/A=12 Me ;
300. 21:7 ~ 1
200
100

 

l

 

 

 

 

50° ? E/A=10 MeV ‘ "1

400 :- z _7 ‘71,
300;- " -:
200;-

100:-

 

 

 

 

 

 

 

600

E/A=8 MeV
21:7 ‘.

NUMh ER OF EVENTS

400

 

200

 

 

 

"T'rj'fi‘l'U

 

 

22

Figure III.2.6 Simultaneous events for 2,:7 between telescope-2 and
telescope-3 (solid line) or telescope-fl (dotted line).

III-54

“Ar + 120, E/A=8 MeV

 

 

25 -
L.
I-
20 I -
L— o o
I. . o o O
I— o o O . O
N _ . o . O O
N 15 I—- o o I O O
10 r
L.
55 I l l l l I ll 1 L1 I I ll
0 2 4 6 8 10 12
21
Figure III.2.7 Z, - Z, correlation plot for simultaneous events between

telescope-2 and telescope-3. Arrow drawn indicates the total charge
(ztot) of the system. a) At E/A=8 MeV.

 

III-56

40Ar + 120, E/A=12 MeV

25:
\ ;
ssgs
I fill
5:1llllllllllJ

 

 

10 12

O
N
4;
03
CD

Figure III.2.7 (cont'd.) c) At E/A:12 MeV.

III-57
where ECM+Q consists of the excitation energy of the compound nucleus in

the full-momentum transfer reaction, and E and E represent

Coul’ EDef’ Rot
the Coulomb potential, deformation energy, and rotational energy it] the
scission configuration, respectively. The typical values of ECoul and

(ERot) are 22 and 14 MeV, respectively, for the near-symmetric fissions,
and the liquid-drop model predicts the deformation energy to be about 20
MeV [RoBM]. Therefore, the estimated average excitation energies in the
scission configuration are about 38, 56, and 74 MeV at E/Az8, 10, and 12
MeV, respectively. If half the excitation energy is taken by each
symmetric fission product, the average excitation energy of 19 MeV taken
by one fission product at E/A:8 MeV may be large enough to emit 21.1ight
particle. innis would be emission of a nucleon or alpha-particle
depending on the excitation energy and the spin of the fission pnxmduct.
The 18 MeV difference in the excitation energies between the neighboring
beam energies which were employed in the present experiment may
correspond to the elimination of approximately one charge (or about 2
mass-units in this mass region). This prediction is roughly consistent
with the data, which implies that the lower average values of Z,+Z2 for
the higher beam energies does not demonstrate the onset of incomplete
fusion.

The events with lighter fragments (smaller 2,) show a wider range
of 22 with smaller values of Z,+Z,, and the range becomes narrower for
heavier fragments (larger 2,) while the value of Z,+Z2 becomes larger.
A lot of events with the total charge, 2:24, was observed at E/A28 MeV,
especially for 2, close to half of the total charge, however the rnunber
Iof such total charge events decreases dramatically relative to those of

less than the total charge at E/A:1O MeV and 12 MeV. Efiuu events with

III-58
the total charge are observed for Z,<6 at any beam energy, and this may
be due to either the sequential evaporation decay of more light
particles after binary decay from the compound nucleus or the direct
binary-decay process after incomplete fusion. The population
distribution of nuclear states by measurement of the gamma-ray
intensities in coincidence with these complex fragments will be
discussed in Chapter IV.

In the case of incomplete-fusion reactions, because the
participants from the projectile and the target to form a composite
system are, in general, different from those for the complete-fusion
reactions, the moving source does not coincide with the center-of-mass
frame but deviates from it. This was checked by determining the
centroids of the Lorentz-invariant differential cross section 3;, 303v o

the heavy residual fragments and comparing these with the velocity

 

f

VCMcoselab'

velocities for K and Ca are in good agreement with VCMcoselab; however

that for Ti is significantly lower than expected while that for Sc

Figure III.2.8a shows that at E/Az8 MeV, the centroid

remains roughly in agreement. The solid lines represent the predicted

velocity (v coselab) and the arrows indicate the centroids of the

CM
Lorentz-invariant differential cross sections. A similar result at
E/A=10 MeV is shown in Figure III.2.8b. A general tendency one may
observe in these two figures is that the centroid velocity decreases as
the mass of the fragments increases. This can be considered as a strong
indication of the tendency toward projectile break-up in incomplete
fusion. A shift in the centroid velocity away from the predicted

velocity may be used to estimate the fraction of the complete-fusion

cross section to the total reaction cross section [H187, MoBlIb].

III-59

However this becomes less plausible under the circumstance of decreasing
centroid velocity with increasing mass in the heavy residual fragments
region. The possible errors caused by the use of one less or one more
unit of mass could not explain the discrepancy, and this becomes a
puzzle if one compares this result with that in Ref. M0811b. In this
reference, Morgenstern et al. showed a preference for the breaking—up
the lighter nucleus (target nucleus in this case) rather than the
heavier nucleus during the incomplete-fusion process in a dinuclear
reaction. This may be supported by an argument in the abrasion model,
that the breaking-up of the smaller nucleus, rather than the larger
nucleus, involves a smaller surface area in the process of shearing away
the occluded volumes [018%]. The centroid velocity of residual
fragments with mass A:II3 from the reaction ”Ar + ”C at E/A213 MeV in
this reference is higher than the center-of—mass velocity at Glab=6°,
which implies that the incomplete-fusion process is mainly due to the
break-up of the target nucleus. Similar but more specific results are
presented in Ref. M086b. The higher centroid velocities obtained in the
the particle inclusive spectra for the heavy residual fragments from the
reaction ”Ar + ”C at E/Az'l MeV have been regarded as being due to the
massive cluster transfer in the entrance channel. Those heavy residual
fragments were detected at O=2.5°, and this angle is much smaller than
that employed in the present experiment. Nevertheless, disagreement
between the data from Refs. MoBllb and M086b and the present experiment
may not be explained without further information on the cross sections
of evaporation residues with a wider mass range at the various angles.

One of the most interesting features one can notice in the Figures

from III.1.3a to III.1.3c is the change in the detected yield of heavy

III—60

40Ar(12C,X), E/A=8 MeV, 11°

 

 

 

 

 

 

 

I- I—
. , .
I. K T1 .
t I —. 6III
I— : ""1 l“,
IE II L 1"“ I
p :— : "WI," II,
CD : L "'1'" "
A . : I .
m : » .
c: +9 WI]l...11.11;.111l121m111111..l.'....1111.l....
(O a :
E 5 “A!" ”C I
I "I.
m if L r ',.
CD «1 - : "I "
I- '— I I
N 4&3 _ : '1' '1
“H _ " .'IOI "
p a . E ' 'I
\ <3 ....1....I...1....1....1....-.1.1.1 I I...1I....I....
v - '
F-I I L
. , I C]. ,,,,,.,.-,.,.,, I C a ....
I... , """"" ' "a. :
: """ " I' II
I" .-
L T
:..1.1..441...I....I....I‘....’1..I....-1...1....1'1".1..I....

 

 

 

 

 

 

 

0.08 0.09 0.1 0.11 0.12 0.08 0.09 0.1 0.11 0.12
”U / C

Figure III.2.8 The Lorentz-invariant differential cross sections for
heavy residual fragments. a) At E/Az8 MeV.

III-61

40Ar(12C,X), E/Ale MeV, 110

5-01 ECa

: I'I" *-

h . fl 5

_ '1 I-

. u .

: ,u“ II H'. I N
. I —

I
1' 1
1‘.
l. I l I I' l l l
11 1111 1LJ1 1111 llllll 1 1111 1111 1111 1111 1J_11
P

 

 

 

 

 

(Arbitrary units)
,2

(1/v2)620/606v

 

 

 

 

 

 

 

’ "' 'I I
'I
— 'I b '
l I. ,' l
.. 'l '
I- 'I' I.
_ '
I. I-
. l .1
b I.
D
p . ' b ...I g
I' 'l I I I ’ "‘I . . . I l I
111111111111111111111111 clogl 1 1111 111.1111 1111

0.08 0.09 0.1 0.11 0.12 0.09 0.1 0.11 0.12 0.13

Figure III.2.8 (cont'd.) b) At E/A=1O MeV.

III—62
residual fragments close to the compound nucleus (52Cr), such as V, Ti,
Sc, etc., which may indicate the increasing role of incomplete fusion
with increasing beam energy. Further discussion of this may be obtained
by comparing the data with the predicted kinetic energy spectra fkn~ the
heavy residual fragments by a statistical model,1kn-example, LILITA
[6081]. He omit this discussion in this thesis because c”? the latw<<3f

the full-ranged spectra for the heavy residual fragments.

111.3 Slope Parameters

iMoving source fits [He82, Ja83] for the complex fragments were not
carried out for the current data because of the limited information
about the angular distributions (measurements were carried out at angles

only from 9 ~10° to Blabz17°). Instead, the results from the velocity

lab
diagrams [Figures III.2.3(a—c)] and the median velocities shown in
Figure III.2.1! provided information on the relation between the moving
source of complex fragments and the center-of-mass frame, i.e., they may
coincide with each other, or they are very close to each other at least.
Possible contributions in the emission of complex fragments from other
sources, such as a target-like moving source or a projectile-like moving
source, must be taken into consideration as the beam energy increases
far above E/A=12 MeV. The kinetic energy spectra in the center-of—mass

frame were fitted by a chi-squared minimization procedure using a

Maxwell-Boltzmann function

_ (E'-C)

N(E') « (E'-C) e T , (111.2)

Ill-63
where T is a slope parameter, and the parameter C is a Coulcmn) barrier
correction. In order to fit the spectra with Eq.(111.2), the low
kinetic energy part of the spectrum was cut off. This nmuhe the effect
of the Coulomb barrier penetration on the slope parameter negligible.
A transformation of the double differential cross secthmw from one

frame to the other was carried out according to the equation [Jo75],

820'(E',Q') _ 820(E,Q) sinO
BE'BO' ‘ asap sinO' ' (Ill-3)

 

 

and the angle correlation was calculated classically as

sin0
sin0'

28CM
B

 

. B 2

= C : 3‘- : SQRTI1+ [-% - COSO] , (111.1-I)
where the primed and unprimed notations represent the center-of-mass and
the laboratory frame, respectively. The velocity of the center-of-mass

frame, B was given as 0.1010, 0.113c, and 0.1240 for E/A=8 MeV, 10

CM’
MeV, 12 MeV, respectively. The velocity of the fragment” [3, was

classically given by

1/2
B : {—gE—-—] , (111.5)

931.5 A
where E is the kinetic energy of the fragment in the laboratory frame
and A is the mass number of the fragment. Under the assumption of an
isotropic emission in the center-of—mass frame, the corresponding
equation to Eq. 111.2 can be obtained for the kinetic energy spectxwi.in

the laboratory frame according to the above transformation as

l

N(E) a C

(Ell;2 - C) e , (111.6)
where C is the function of the laboratory kinetic energy E as defined in
Eq. 111.“.

Curves obtained by fitting Eq. 111.6 to the data are shown in
Figures III.2.1(a-c). The fitting parameters for complex fragments with
332511 are shown in Figure ILIJLJ and are tabulated in Table III.3.1.

In this table,i§ refers to the calculated Coulomb barrier in the

Coul

center-of—mass frame, and the values of E are presented to compare

Coul
with the fitted value C. A notable feature in Figure III.3.1 is the
decreasing slope parameter as the mass of the fragments increases.
Target-like fragments, which may have been produced via quasi-elastic
scattering, inelastic scattering, or direct nuclear reactions in this
reverse-kinematics reaction, are generally backward-scattering fragments
in the center-of-mass frame, hence implying no significant role of these
fragments on the larger slope parameters for the lighter fragments. One
can note that this behavior is consistent with the time evolution of the
temperature in a hot-equilibrated nuclear system studied by Boal.<3t al.
[8086]. Boal et al. predicts a rapid change in temperature at the early
stage. If most of light particles were emitted at the very early stage
of the thermal equilibrium while massive fragments were emitted from the
expanded nuclear system at a later stage, then the variation of the
slope parameters as a functhxicn‘nmss (i.e., a smaller slope parameter

for the lighter complex fragments and vise versa as shown in Figure

III.3.1) becomes plausible.

III-65

 

 

 

 

4.5 L -
4.0 r _ _
A * I’ j
% _ .
3.5 ~ -
2 . ~
~~../ [ ""1I~“'_,II :
L21 * i
[L 3.0 :-
0 ~ .
fi : :
2.5 — , a
: O E/A=12 MeV ,
. I E/A=10 MeV ‘6 3
2.0 f o E/A=8 MeV j
'1 l l l 1 1 1 l l I 1 l l l

 

7Be 10B 12C MN 160 19F 21Ne
986 118 13C 15N 170 20F 23Na

Figure III.3.1 Slope parameters for complex fragments. Lines are drawn
for the eye-guide.

III-66

Table III.3.1 Kinetic energy spectra fitting parameters for complex

 

fragments.
E15 _Is_o_t_o_.2e. 502111 __c_ 2222
(MeV) (MeV) (MeV) (MeV)
8 7Be 11.6 11.5 3.30:0.15
9Be 10.9 12.2 3.2910.20
‘°Be 10.6 11.5 3.54:0.20
‘°B 12.6 14.0 3.24:0.18
“B 12.2 14.0 3.28:0.16
‘ZC 13.5 14.1 3.7110.32
"C 13.1 13.8 3.47:0.29
‘“N 14.0 15.3 3.0510.10
‘SN 13.6 14.3 3.19:0.39
“O 14.2 14.8 2.95:0.08
‘70 13.8 14.5 2.97:0.15
‘9F 13.6 14.3 2.68:0.14
2°F 13.2 13.7 2.71:0.18
Z‘Ne 13.2 14.9 2.09:0.31
10 9Be 10.9 11.4 3.77:0.47
‘°B 12.6 13.3 3.98:0.28
“B 12.2 13.5 3.90:0.19
12C 13.5 13.7 4.1910.37
'3C 13.1 13.4 4.22:0.53
‘“N 14.0 14.6 3.89:0.63
‘5N 13.6 14.0 3.7010.57
1“0 14.2 14.1 3.49:0.35
‘70 13.8 14.1 3.42:0.40
‘9F 13.6 13.9 3.37:0.50
2°F 13.2 13.4 3.55:0.75
21Ne 13.2 14.4 2.65:0.39

Table III.3.1 (cont'd.)

III-67

 

E15 Isotope
(MeV)

12 ‘°B

ZJNa

M

(MeV)

12.
12.
13.
13.
14.
13.
14.
13.
13.
13.
13.
12.

-JU”11\.)O\

@NNO‘CDNO'NO

_ m

(MeV) (MeV)

13.5 4.04:0.18
13.1 4.32:0.58
13.2 4.47:0.41
13.2 4.44:0.38
14.1 4.43:0.35
13.2 4.35:0.52
12.9 4.0510.57
14.0 3.68:0.54
13.9 3.46:0.93
13.2 3.47:0.51
13.9 3.21:0.45
14.4 2.97:0.48

 

Table 111.4.1 Nuclear temperatures in the

(units in MeV).

Fermi gas model

 

 

E/A E

8 94.2
10 112.7
12 131.1

KT

 

3.44
3.76
4.06

33.
36.
36.

R
4 60.8
1 76.6
1 95.0

2.76
3.10
3.46

 

a) Average temperature with rotational energy taken into account.

III-68

111.4 Fermi Gas Model

The slope parameters obtained from the Maxwell-Boltznmun1 function
in the center-of—mass frame were compared with the temperatures
predicted by the Fermi gas model for this reaction. The relationship

between the excitation energy, E*, and the temperature, KT, is given by
E* = a(kT)2 , (111.7)

where a is the level density parameter. The level density parameter has

been defined by TSke et al. 11681] as

a = TEEET(1+3.114a'1/3r2+5.6261‘2/3F3+...] (MeV-1) , (111.8)

where A is the mass number of the compound nucleus and the quantities F2
and F3 are set to be unity under the assumption of a spherical shape.
The calculated value of the level density for 52Cr from Eq. (111.13) was
6.53 (MeV-1).

The average thermal excitation energy of the equilibrated compound

nucleus with an average angular momentum, <Q>, is given in Ref. M086a as

- *.
<Eth> - E (ER) , (111.9)

hence the average nuclear temperature becomes

(KT) = ( <1:t > / a )1/2, (111.10)

h

III-69

where (ER) is the average rotational energy of the rotating compound
nucleus. The calculated average rotational energies and the average
nuclear temperatures are given in Table 111.4.1. The predicted
temperatures here are comparable to the slope parameters given in Table
III.3.1, and these will be discussed further in Ch. IV in comparison
with temperatures obtained from the population distribution of nuclear
states.

In order to calculate the average rotational energy in Eq. 111.9,
the average angular momentum for the compound nucleus was calculated
from the predicted critical angular momentum by means of the sharp
cutoff approximation. 1n this approximation, 3 partial-wave cross
section with an angular momentum 11 is given by 0Q«(2Q+1). The maximum
angular momentum of the compound nucleus was calculated by assuming a

1/3 + A21/3). The result for 52Cr

maximum impact parameter of 1.2(AI
shows that Qmaxz39, 44, and 4919 at E/A28, 10, and 12 MeV, respectively.
On the other hand, a critical angular momentum for the same nucleus, at
which the shape loses stability against the tri-axial deformation mode,
is predicted to be 21:32 h [Si86, C074]. Another critical angular
momentum, at which the system loses stability to fission and beyond
which no equilibrium shape exists, is predicted to be 211243 h [3186].
In Ref. 8186, inclusion of finite-range effects in the nuclear surface

energy lowers the predicted Q for the light systems as compared to the

II
rotating liquid-drop model predictions [C074]. A value of 1211:52 11 is
predicted for “Cr in the rotating liquid-drop model [C074]. In this
thesis, ch=43 h is adopted [P1177] as the critical angular momentum for

complete fusion to form 52Cr, and the maximum angular momenta calculated

in Table 111.4.1 are limited by this value.

III-70
Fusion reacthmusrmve been predicted to occur at distances well
(NJtSide the point of contact between two colliding nuclei [Ba74, Wi73I,
where the nuclear densities in the overlap region add up to saturation
density of nuclear matter. This implies that the critical angular
momentum for complete fusion of 52Cr may be larger than 43 h. Also, the

1/3+A21/3)+2 (fm) increases the

use of a distance parameter of r:1.2(A,
maximum angular momentum far above the adopted critdixil angular
momentum, 43 h. 0n the other hand, some authors [M086b, Ni80] suggested
that the critical angular momentum for complete fusion to fknun 52Cr be
as 11nd as 32 h. From any point of view, the underlying physics is that
the onset of incomplete fusion, therefore, may occur at beam energies
much below E/A=8 MeV. Incomplete fusion will compete more strongly with
complete fusion in peripheral collisions than central collisions. One
should note that the maximum angular momentum of the compound nucleus
calculated with the sharp cut-off radii of the nuclei is somewhat
artificial. Also which maximum angular momenmnntx>use in the
calculation of the corrected Fermi gas model temperatures is not very

significant as the rotational energy in the heavier system changes

little with the increasing or decreasing maximum angular momentum.

CHAPTER IV: POPULATION DISTRIBUTION I

(COMPLEX FRAGMENTS)

IV.1 Introduction

The primary population of a nuclear state in thermal equilibrium
should depend only on the temperature of the system, the excitation
energy of the state, and the spin of the state. The rathaiicfi‘the

primary populations of two states in thermal equilibrium is written as

__ (12.-E.)
R = g-gfl—Be “T , (IV.1)

where J1 and E1 represent the spin and excitation energy of the state 1,
respectively, and k'I‘ is the nuclear temperature. The fraction of the

total population fn in a given state can be deduced from Eq. (IV.1) as

-E /KT
(2Jn+1) e
fn - -E./KT ’ (IV'2)
{(2ji+1) e
l

 

where the denominator is a partition function, and the summation over'i

includes all the states of the nuclear system.

In general, the half-lives of the gamma-ray emitting excited states

IV-71

IV-72

are so short that the nucleus is in its ground state when it reaches a
particle detector. The population of the excited states can be measured
with a new technique employed by Morrissey et al. [M084a, M085a, M086a].
In this new temperature measurement, the relative populations of excited
states were measured by observing gamma-ray intensities in coincidence
with light fragments, such as “Li, "’Li, “Li, 7Be, and ”B. The gamma-
ray detectors measure the excited state populations which include the
feedings from the higher-lying states, while the particle telescopes
detect bothithe ground and excited states of nuclei. A gamma—fraction,
the fraction of the fragments that emit a specific gamma-ray by a
transition from one state to the other in a nuclear system, can be
determined experimentally in a particle-gamma coincidence run as

NY BIC.LIVE(singles)

eY NP BIC.L1VE(coincidences) ’ (IV-3)

 

FY:

where NY is the total number of counts in a specific gamma-ray, e is

the efficiency of the gamma-ray detector, N

Y

P is the number of inclusive
fragments detected during the particle-singles runs, and the term
"BIC.LIVE" refers the integrated beam current during the measurement
runs.

In the limit that feeding from particle unstable states in higher-A
nuclei is unimportant, then the fraction of nuclei that.£flnit the

specific gamma-rays by a transition from a state m to another state 11

can be formulated as

IV—73

— Em/KT

[(2jm+1)e + Mm]

m,Q - E./KT '
[(2Ji+1)e

1

 

(IV.4)

and the feeding from the higher-lying states to the state m, Mm, it) the

same nucleus is defined by

E - Eq/KT

M : a [(2j +1)e + M ] , (IV.5)

m q:m+1 q,m Q Q

where (11 J is the branching rathacfi‘the gamma-ray transition from the
7

state i to the state 3, and the feeding Mq must be repeated up to the
highest lying state that decays through gamma-ray emission. The effects
of feedings by sequential decay of higher-A nuclei is discussed later.
Eq. IV.4 may contain somewhat large uncertaintnfisii‘the information
regarding energy and spin of the levels and the gamma-branching ratios
is iruxnnplete or ambiguous. Nevertheless, by simply equating Eqs. IV.4
to IV.3 one can determine the temperature KT, which is the only unknown
parameter in those two equations. In the simplest case of a nucleus
which has only one bound excited state, for example, 7lj.auui 7Be, Eq.

IV.4 can be simplified as

- E,/KT
F : (2j1+1)€ (111.6)

1'0 1(2J.+1) + (21.+1)e‘ E‘/KTJ

 

where j. and J, are the spin of the ground and the excited state, and E,

is the energy of the only bound excited state.

IV-74

IV.2 Data Analysis

The essential key to this measurement is a clear identification of
the ixuiividual nucleus in the complex fragment region. Doppler shift
corrected histograms of gamma-ray energy spectra were generated for each
particle-gamma coincidence combination. The Doppler shift corrections
are in the range of 3 ~ 13%, depending on which paii~<1f particle
telescopes and gamma-ray detectors was chosen. The estimated
geometrical error due to the finite solid angle of the Ge counter, which
is based on the average kinetic energy <v>=0.19 c of the light
fragments, was roughly 2.4 ~ 4.2%, depending on the angle between the Ge
counter and the particle telescope. Since this value hsrmuflilarger
than the resolution of the Ge counter, the gamma-ray energy spectra of
the NaI(Tl) scintillation detectors were much more useful for light
fragments and intermediate fragments (the geometrical shape of the
NaI(Tl) detector was not an important factor due to the large distance
from the target and its large resolution). A random coincidence
histogram of the gamma-rays was subtracted from a real coincidence
histogram of the gamma-rays for the same combination of the particle
telescope and the ganma-ray detector, however the ganma-ray count in the
random coincidence histogram is very small as compared to that in the
real coincidence histogram (typically less than 5%), as mentioned in Ch.
11. To improve statistics in obtaining the number of counts of the
specified gamma-rays for further calculations, all the histograms from
the NaI(Tl) detectors were summed together after having been corrected

for random coincidences.

IV-75

IV.3 Light Fragments

Doppler shift corrected gamma-ray energy spectra in coincidence
with light fragments are shown in Figures IV.3.1(a-c) for the respective

beam energies. The peaks of E :478 Kev for 7Li, EY:429 Kev for 7Be, and

Y

EY:718 Kev for ‘°B are clearly seen at all the beam energitns. The 414
KeV and 1022 Kev gamma-rays from '°anwzrelatively weak gamma-lines,
and are not clearly observed in the present experiment. No prominent
gamma—ray peaks for 6Li, 9Be, and “B were observed in the present
detection range as expected from the level structure [A384, Aj85]. 'The
511 KeV positron annihilation gamma-rays were widely spread after the
Doppler shift corrections and were negligible quantitatively in most
cases. The majority of the coincidence gamma-rays observed in the
present experiment consisted of continuum gamma—rays with an exponential
tail at the high energy region. This was interpreted as being due to
one broadly defined moving source of the continuum gamma-rays, and the
underlying statistical transitions are extended over the entire range of
the data.

The gamma-ray peaks under consideration were fitted with a Gaussian
function to obtain the number of counts in each peak. The gamma-
fractions determined by Eq. IV.3 are compared with those calculated with
Eq. IV.4 with temperatures predicted by the Fermi gas model, and the
results are shown in Figures IV.3.2(a-c) for 7Li, 7Be, ‘°B,
respectively. The solid curves drawn in Figures IV.3.2(a-c) represent
the gamma-fractions predicted by the Fermi gas model. The decay schemes
of the particle bound states for each nucleus are drawn in these

figures. As discussed in Sec. 11.4, the contamination of the 7Li

IV-76

12C(40Ar,7X), E/A=8 MeV

 

200 I

50

0
80

60
40
20
0
400
300
200
100

COUNTS PER CHANNEL

Figure IV.3.1

150i
100'

1

 

 

 

 

 

_ 10B _
0.718->G.S.
_ / -
' 1 . . 1 1
: , . . . . , . . , 3
L A/ 0.429->G.S. j
E '7 3
3- Be -:
: l . . . 1 1 1 . . I I
, I ' ' ' ' 1 ' 1 .
:- / 0.478-rG.S. “I
L '7 . .3
E L1 3
. . l . 1 . 1 l . . . I . . ‘
50 100 150

CHANNEL

coincidence with light fragments. a) At E/A=8 MeV.

Doppler-shift corrected Y-ray energy spectra (NaI)

COUNTS PER CHANNEL

150

100

50

0
100
80
60
40
20

0’
200:

150
100
50

IV-77

 

12C(4OAI‘,7X),

I f fi—

E/A=10
/

l A A 4A

1

0.718->G.S.

MeV

10'
B

-1

_

-

 

IITY'YI'UVV'VVVV

 

~1-

‘—

A l A A

50

A A
I ' I W V V U

0.429 G.S.
/ -)

A A A A l A A I
V I V V l V

.4/ 0.478-»G.s.

. 1 . .

100

CHANNEL

Figure IV.3.1 (cont'd.) b) At E/Az10 MeV.

‘—

 

IV—78

12C(40Ar,7/X), E/A=12 MeV

l

 

500 C
400 g—
300 f. / 0.718-»G.S.
200
100
200 0.429403. 4

/

L 7 ..
150E I363
100:- -§
50 g— ‘
O _ . : t t . . . :
250g 3, 0.478408. ~;
2003— 7 . -f

1 L1 2
150; 7
100;- -‘
50 g- '

O : . 1 1 . l 1 I . 1 1 . . .
50 100

CHANNEL

7' I

10E;

A A A A A A l A A A
U I V I I V l v '

 

-_

AAA AAA

A L l A A A A
I V l r U r ‘r

 

—1—
.11—

COUNTS PER CHANNEL

 

 

l A

150

Figure IV.3.1 (cont'd.) 0) At E/Az12 MeV.

IV-79

 

0.4 s,....,....,....,....,.

-—
—_-—_
’-——-

.0
00
1
1
I
1
1
l

 

CD
00
l
..{p..
1

(“*0
1/2‘ 0.470

 

y—FRACTION

P
H
I
l

 

3/2' G.S.

 

 

 

0.0.11....1....1....1....1.l
6 8 IO 12 14

E/A (MeV)

Figure IV.3.2 Y-fractions. Dashed line represents the predicted Y—
fractions with the Fermi gas model temperatures. Decay schemes are from
Refs. Aj84 and A185. a) For 7Li.

1V-80

 

0.4 I I l I U I I l I U I I l l I I I I U U I I l I

03: ------- "‘“ ‘

7—FRACTION
—o—

 

0.1 ‘ ‘

 

 

 

 

 

0.0 .1....1....1....1....1..
6 8 10 12 14

E/A (MeV)

Figure IV.3.2 (cont'd.) b) For 7Be.

IV-81

 

V V
0.5 l I I U I' I V U U T I V I I I l U I U U l I
D

l 1
’ ‘ ‘l
-
fl
’
’
“
I ’
’
’

’
I —’
fl ‘
fl
’
"
04
0 ’
d

 

 

 

 

 

 

 

 

 

0
1—1 '
B 0.3 — —
an: 2. _(g) (on) (a) «1 5.1“ ,
IT. 02 _ 2., (u) (m (to) 3.58,, _
5 1., I, (is) (1m (81) 2.51 4
_ g 0" (m) 1.740 .
0-1 _" 1* I’ mo) 0.710 "
3* 1' 0.3.

 

10 1
. B .
0.0 1 . I . . I . I 1 . . . I . . . 1 I . . . I I . I
6 8 10 12 14

E/A (MeV)

 

 

 

Figure IV.3.2 (cont'd.) c) For ‘°B.

IV-82

 

10.0 1 l r I 1 1 I 1 1 I 1 1 I 1 1 I 1 T 1 1 I 1 r
1- d
h- -1
h d
I- d
5.0 - -

 

 

 

 

 

 

 

 

 

 

 

IcT (MeV)
. ‘1
1
I
I
I
e 1
.9—

 

 

 

1.0 :— __J
0.5 - _
_ 0 "Li(0.478->G.s.) _
>< 7Be(0.429->G.S.)
D 1°B(0.718->G.S.)
().1 1 I .L,1 1 l I 1 1 1 1 I 1 1 1 1 I 1 1 L 1 I 1 1
6 8 10 12 14

E/A (MeV)

Figure IV.3.3 The observed temperatures from the Y-ray transitions in
the light fragments. See the text for the lines.

IV-83

Table IV.3.1 Deduced nuclear temperatures from 7L1, 7Be, and ‘°B.

 

 

 

 

E/A Isotope EY Decay rca) NY 1

(MeV) (KeV)

8 ’11 978 0.H8+g.s. 0.296 12201100 0.28710.02u
7Be M29 0.u3+g.s 0.300 220130 0.27910.038
‘°B 718 O.72+g.s. 0.397 M73180 0.31710.05u

10 7L1 H78 0.u8+g.s 0.300 230130 0.29110.038
738 M29 0.93»g.s 0.303 260130 0.29010.03u
‘°B 718 O.72+g.s. 0.912 599190 0.u0610.062

12 7L1 H78 0.98»g.s 0.303 670150 0.20u10.016
7Be 929 O.N3*g.s 0.306 550150 0.23810.022
‘°B 718 O.72+g.s 0.129 15721190 0.37u10.0u6

KT
(MeV)

+2.
-0.
+9.
-0.

+0.
'6 -O.

:UWGDOQUO

+20
-1.
+7.
-0.

O‘O‘OON

-0.

+0.11
-0.10
+0.29
.91_0.
+0.“
-O.3

.72

 

3) Predicted gamma-fraction. See the text for detail.

IV-BU
singles inclusive spectra by the ground state of 8Be [14072, 8186] is
taken into account in determining the gamma-fraction fkn~ 7Li. Ifiar the
nucleus ‘°B, there are a few unbound states above the particle threshold
energy (11.116 MeV) which decay partially by gamma-ray emission [F066,
Ne70, Re72, AJBH]. However, only the 5.1614 MeV state has a comparable
ganma-width relative to the total decay-width (FY/P2871 for the 5.164
MeV while PY/F<1% for the other unbound states hi ”T3[AJ8H]). Since
the half-life of the 0.718 MeV state in ‘°B is about 1.02 ns, which
corresponds to a 5 cm flight distance on the average at E/A=10 MeV,
errors which may be caused from the change in geometrical efficiencies
of the gamma-ray detectors and also from the wrong Doppler shift
corrections must be included. Although the estimation of the change in
the geometrical efficiency of the gamma-ray detector becomes a
formidable calculation because of the cylindrical shape of the crystal,
a rough estimate gave a possible error of 10% from these sources, and
this was combined with the statistical uncertainties for ”B. As one
may see in Figures IV.3.2(a-c) and as Morrissey et al. pointed out
[M08‘4a, M085a], the small energy level spacings of these nuclei limit
the sensitivity of their population distributions to temperatures of a
few MeV or less, especially for 7L1 and 7Be. This indicates that a fknv
percent change due to statistical fluctuations in the gamma-fraction at
a few MeV temperature, for example, KT=3 MeV, can make the upper limit
of the deduced temperature infinity. In terms of this sensitivity
problem, ‘°B is a better probe of statistical equilibrium than the other
two nuclei under consideration because it has a wider level spacing, and
also feeding from the higher-lying bound states to 0.72 MeV state

improve the sensitivity of the gamma-fraction to temperatures.

IV-85

Deduced temperatures for light fragments are plotted as a flnuztion
of the beam energy in Figure IV.3.3. The solid curve drawn in Figure
IV.3.3 represents the predicted temperatures in the Fermi gas model
without correction for the rotational energy, and the dashed curve
represents those in the Fermi gas model with subtracting the rotational
energy from the excitation energy (as described in Section 111.14). The
overall results, which are tabulated in Table IV.3.1, include the gamma—
ray counts (NY)’ the gamma-fractions (f), and the deduced temperatures
(KT) for light fragments. Errors in the temperature are asymmetric due
to the logarithmic form of the gamma-fraction. The statistical errors
and systematic errors in evaluating the gamma-ray counts dominated the
other sources of error. This will be discussed further in Sec. IV.5.

Temperatures at E/A28 MeV and 10 MeV agree well with those
predicted, and this is consistent with the result nifkfih M086a. In
this reference, where the population distribution of states in light
nuclei was studied in a reaction of '2C + 1“N at beam energies including
E/Az8 MeV and 12 MeV, the deduced temperatures at up to E/A=8 MeV, but
not above E/A=12 MeV, agree with the calculated temperatures with the
rotational energy taken into consideration in the Fermi gas model, hence
indicating consistency with the simple thermal equilibrium at beam
energies below E/Az8 MeV. Measurements at E/A=10 MeV are run; included
in this reference; however data in the present experiment indicate that
simple thermal equilibrium may prevail at this energy, too. As shown in
Figure 3 in Ref. Mo86a, subtraction of the average rotational energy
from the excitation energy lowers the calculated temperatures
significantly especially at bombarding energies below E/Az12 MeV. In

contrast, since the bigger compound nuclear system in the present

IV-86

experiment has a larger moment of inertia.than the smaller system in
Ref. M086a, this reduces the fraction of the average rotatitnuil energy
in the excitation energy [e.g., in Ref. M086a, the calculated
temperatures with and without subtracting the rotational energy at E/A=8
MeV are 3.0 and 1.A MeV, respectively, unfile in the present reaction
they are 3.11 and 2.8 MeV]. Figure 3 in Ref. M086a and Figure IV.3.3
show a fair agreement with this argument, except that the temperature of
2.3 MeV from ”B at E/Az12 MeV in this measurement roughly agrees with
the prediction while those from nuclei of A:7 are significantly lower
than that predicted under the assumption of simple thermal (unlilibrium
(in ref. Mo86a, it is shown that the temperatures are independent of the
nucleus at the same energy; this argument agrees with our data atLEi/A:8
and 10 MeV, however it is not true at E/A:12 MeV). This discrepancy may
be due, among other reasons, to the effect of preferential feedilu; from
higher-A nuclear system on the population distribution of complex
fragments, rather than being due to the non—equilibrium effects at
E/A=12 MeV, and this will be discussed further in the following section
(Sec. IV.“) after considering the population distribution of
intermediate fragnmnts. Nevertheless, it was indicated that the
population distributnn1cfi‘nuclear states in light fragments is
dominated by the excitation energy (or temperature) of the equilibrated
composite system in low energy reactions. However the results also show
that the correction made by subtraction of the average rotational energy
from the excitation energy must be taken into account.

0n the other hand, the temperatures given in Figure IV.3.3 show a
self—consistency between a pair of mirror nuclei, 7Li and 7Be. As shown

in Figures IV.3.2(a-b), both the nuclei have only one bound-excited

IV-87

+
state each with the same spin of % , very close excitation energies of
0.478 MeV and 0.1129 MeV, respectively, and the ground state with the

same spin of 3:. Should the preferential feeding of any level by the
decay of unbound higher mass nuclei [112387, M085a, M0811a, St83] play an
important role in populating the light nuclei, it appears to be
negligible at E/A:8 and 10 MeV at least for 7L1 and "Be in the present
reaction. However, one should not exclude the possibility that the
amount of feeding to the excited states and the ground state were
accidentally proportional to the original populations in each state,

although this is not expected from the energetics and penetrability of

these decays.

IV.“ Intermediate Fragments

By virtue of the individual particle identification for
intermediate fragments (up to 23Na) and relatively well known
information for the spin, the excitation energy, and the gamma-branching
ratio of each bound state in this mass region, the temperature
measurement [M086a, M0853, M0811a] based on the population distribution
of nuclear states was applied in the intermediate fragment regime for
the first time. Gamma-rays in coincidence with these fragments were
detected in the NaI(Tl) detectors. Analysis of these data followed a
similar track as that for light fragments. Figures IV.4.1(a-h) show the
Doppler shift corrected gamma-rays in coincidence with 1"N, ”0, ”O,
1"F, “Ne, 2‘Ne. 22Ne, and 23Na, respectively. The gamma-fraction for

each peak was determined according to Eq. IV.3, and is shown in Figures

IV-88

12C (4OAF 7 16N)

 

 

 

 

 

80; ([0. 297(3 )->G..S (2’)]

E 605- E/A 12 M V;
: = e 1

Z ‘wr i
Z 20;- —f
at: 0: 1 I - . ' ' 1 K I
o 305. 1 _
ES 20;- E/A=10 MeV-i
m w? 4
(2‘) () E . 1 , , 1 , , . 1, 1 .1-1i£ullJii.iHIdJstJL :
E-1 i .
2 :ME 1 €
' g 20;- l E/A=8 MeV j
0 10} -
O: .. . . 1 . 1 . . I11 . 41 . III

 

50 100 150

CHANNEL

Figure IV. A. 1 Doppler- shift corrected Y— -ray energy spectra (NaI) in
coincidence with intermediate fragments. a) With “N.

IV-89

12C (40Ar 7’170)

I— [0. 871(1/2*)-»o. s. (5/2*)] _

 

200_
150
100.-
50

I
1

E/A= 12 MeV-j

    
 

 

6°, , E/A=10 MeV":
40E- ~I

I
9

20f

 

O : . : ¢ : § : 1 : : § : : 1 : 1' : : t c I‘
607 , E/A=8 MeV ‘
40_ -j

 

COUNTS PER CHANNEL

 

 

Oi...1...-11.1.1...41_i
40 60 80 100

CHANNEL

Figure IV.A.1 (cont'd.) b) With ‘70.

Ir'Lllr!I.I‘l ‘ I'll-It {[[l (II-Ir ‘IIPIF<(

COUNTS PER CHANNEL

12C (40A? , 7 180)

 

." ""l#"'1"'fir'
125 @- [3.653(4*)-11.982(2*)

 

 

 

 

10°: E/A=12 MeV I "
75 :- ‘
50 g-
25 E-
0 :fii : § : c c : IL : : : : TL? : : : } . : : t I : ‘ ‘ ‘
- 40 _— [1.982(2*) -3
E/A=10 MeV 198-10213
30 1 1 "
20 -':
10 '1
O : : : § : t : : § 2 c : : § : : : : : : : ; : § : ‘ 2
40 1 1
E/A=8 MeV 1 3
30 ‘1
20 1
10 f
O - 1 1 1 1 1 1 . 1 1 1 1 L 1 1 . 1 1 1 1 1 1 1 1 1 1 ‘

 

 

40 60 80 100 120

CHANNEL

Figure IV.A.1 (cont'd.) 0) With "0.

200 '

50
40
30
20
10

50
40
30
20
10

COUNTS PER CHANNEL

IV-91

12C (40Ar , 7 19F)

 

150 .
100C
50 Z-

; EB//!1==2123 104(3‘]

011%.

1

1—

[1.346(5/2')-10.110(1/2')] '3

1

l I
A A A A l A A A A l A 1A A
v r v v v

 

 

 

 

l U I V r I V I I V

I

q

1

q

1 E/A=10 MeV «

1

’ -
b
I
h

h -
I
b
b
b
D
D
I

I .

V l V I V I V V V V l U V V V I V V T‘

1

b q

: 1 E/A=8 MeV :

b 1

4

q

1

D -
i
:
b
h
D
D
b

b -

I 1
b

4 I J J l A A A A l A A

 

 

0'

40

6O

80 100 120

CHANNEL

Figure IV.A.1 (cont'd.) d) With "F.

200 -

150
100
50

20

20

COUNTS PER CHANNEL

10

Figure Iv.u.1

40:
30'

10.
253

15.

IV-92

12C (4OAI‘ 7 ZONe)

E/A=12 MeV [1. .634(2;)-DG. ..3 (0+)]::

 

V V V V V I V V

 

-
qb

A I A A A
V r V V

E/A=10 MeV 1 -i

V V V V V I V V V

l j 1‘ A A l A
V I V V V V I r V V V l V

1 E/A=8 MeV I

 

b

D

-

I

b

b

’4 A l A L A A l L A A A l A A A A L L A L J

40 60 80 100 120

CHANNEL

(cont'd.) e) With 2°Ne.

 

IV-93

12C (40Ar 7 ZlNe)

800 ' '1‘ [0. 351(5/2+)-’G,S.(3/2+)] I Y _:

 

A I

 

 

 

 

 

 

A 600 E/A=12 MeV ¢ ¢ j
m x 6 3
Z 400 €
Z 200 '
< O : : % t : : : % : c 4 t % : c : : § 2: ; ; I ‘
m 200 6 [2.366(9/2*)-»1.746(7/2")]
C.) 3
DZ. 15° E/A=10 MeV * x 5 ‘3
m 100 "
D-I 50 :- ‘
m 1; ¢ § j : : : } : : : ‘ } ¢ : : : } : : : . _‘
E—' 15% E o [1.746(7/2“) ‘
Z 100; \L +0.351(5/2*)]‘:
:3 75 :- E/A=8 MeV 6 *1
I X 4 :
8 50 g + ‘3
25 :- I

O : L ‘ l . . ‘ A l _ , , . l . . . . . . . .
50 100 150 200 250

CHANNEL

Figure IV.H.1 (cont'd.) f) With 2‘Ne.

IV-9l-l

12C (40A? 7 22Ne)

 

 

 

 

 

 

 

zoo;- E/A= 12 MeV [1.2-my)
S 150 :_ { -)G.S.(O+)] -
Z 100 E ‘
Z 50 g- '
g 0 : f c r : % : ; t = % ¢ ¢ ‘ 3 § : ° ° ° % .
60'- “L
o ; E/A=10 MeV :
m 40} '5
El 20: 3
0-4 L 1
m 0 : i 4 : ' ' ' l A g E .
E2 30} E/A=8 MeV 4
D 20} l €
0 g 3
C.) 10 7 €
0 ' 4 ' 4 L ‘ L '

50 100 150 200

CHANNEL

Figure IV.H.1 (cont'd.) 3) With 22Ne.

IV-95

 

12C (40A? , 7 23Na)

 

 

 

 

 

 

E r . v I ' ' V ' I I r fi
500 L \ [O.440(5/2+)-»G.S.(3/2+)] -
l-—] E .—
EIJ 400 I— p r‘ _:
z I Q g :
Z mm? %§ €
<1: E E/A=12 MeV S v: :
:3: 2007 EL ? %
b +
O 100 - W
m 0 : : ‘fi; # } ¢ : : : § ; : : : : .L : + ; i : ; ; L:
Lil $
D" 50 1 [2.704(9/2*)+2.076(7/2+)] -‘
m :
E ;
:3 v E /A= 10 MeV :
O l :
O <

 

 

 

 

100 150 200

CHANNEL

Figure 1v.u.1 (cont'd.) h) With 23Na.

IV-96

 

, **r*r ' l ' I r] ' r r ‘
(L6 _ -
(297 + 276)

 

 

 

 

7—FRACTION
4

(L2 -

NO'GI‘

 

 

 

 

0.0 A A I PL A A l A A A A A A A A A A
6 8 10 12 14

E/A (MeV

Figure IV.1I.2 Y-fractions. Lines are the predicted Y-f‘ractions with
the Fermi gas model temperatures. Decay schemes are from Refs. A383 and
A186. a) For “N.

7—FRACTION

Figure IV.4.2 (cont'd.)

' I r T I I l r T .1
o 5 ' 4.1436 1"0 + n _‘
. _ (100) .

5/2 3.341

_ (100)
1/2 I 3.055 -
0'4 _ 1/2“ (100) 0.371 _
5/2” G.S. 4
17 1
. O .
0.3 ‘
(341) ______
0.2 " — -
.4
0.1 . + ‘
O O b l A . l . A l . L A l . l . 1
6 8 10 12 14

IV-97

 

 

 

 

 

 

 

 

 

 

 

 

b) For ‘70.

E/A (MeV

IV-98

 

U l V T V I I I I I I l T U V U I I I V I l I

_ 18O o 1.982->G.S.
1.25 - 0 3553-4982
2
O 1.00 : ________________________
,_, .
B L
(<31) I
0.75 -
0:
LT
50.50 -

 

 

I ‘ o (L
- I 2%

 

 

 

O’DobL1....1....1....1....1..
6 8 10 12 14

E/A (MeV)

Figure IV.N.2 (cont'd.) c) For ‘°O.

0.3

0.2

7—FRACTION

0.1

0.0

IV—99

 

——-——‘
'—

 

19F (1.346»0.110)

 

L I l 1 l J l J l 1 A I L l 1 1 I L j 1 l

 

6 8 10 12

E/A (MeV

Figure IV.H.2 (cont'd.) d) For ‘9F.

14

 

IV-100

 

1.0 I I I I I I I I I I I I l I I I I I I I I I I I

 

 

7—FRACTION

(l4 - 1+ _

0.2 '-— 20 _
- Ne (1.634»G.S.) -

 

 

 

(10 b .1 .. . .l .1 l. l .. .. l. . .. I.
6 6 10 12 14

E/A (MeV

Figure IV.H.2 (cont'd.) e) For 2°Ne.

 

IV-101

 

I l I I I I I I I I I l I I I I I I

1.0 __ ZlNe o O.351—>G.S.
' o 1.746->O.351
I 2.866->1.746

0.8 -

0.6 —
~ ¢
0.4 — J)

7—FRACTION

 

 

 

 

A l l l 1 l l 1 L l I 1 1 l l l l l
0.0 '

Figure IV.H.2 (cont'd.) f) For 2‘Ne.

IV-102

 

 

 

 

 

1.00 '—
z """"" F
.2
0
<2 { +
Dd
LTl-I 0.50 —
A
0.253-
' 2ZNe (1.275->G.S.)
0.00..l.l..l....l...il.. I.
6 8 10 12 14
E/A (MeV

Figure IV.4.2 (cont'd.) 3) For 22Ne.

 

IV-103

 

I I I T I I I I I I I I I I I I I I

I 0.440->G.S.
O 207640.440
0 270462.076

0.8 '- +

0.6 -

7—FRACTION

 

0.2 '-

 

 

D
O O 1 I 1 1 1 1 l 1 1 1 1 l 1 1 1 1 I 1 1
a

Figure IV.4.2 (cont'd.) h) For 23Na.

 

IV-1014
IV.4.2(a-h). The superimposed curves drawn in Figures IV.4.2(a-h) are
the predicted gamma-fractions for the observed gamma-lines by means of
Eq. IV.4 with temperatures predicted in the Fermi gas model. Errors
included in these figures are mainly due to the statistical
uncertainties and the systematic uncertainties, which will be discussed
in Sec. IV.5. The possible errors in the level information were
ignored. The characteristic of each nucleus regarding the information
about the level and gamma-branching ratios and the observed gama-rays

is as follows:

a) :91. There are 3 excited states below the neutron-threshold energy,
2.1491 MeV, as shown in Figure IV.ll.2a. No state above this threshold
decays through the emission of gamma-rays [A186]. A gamma-ray peak of
EY=297 Kev [0.297(3-) + 0(2')] in Figure IV.1l.1a was not separated from
EY=276 Kev [0.398(1’) + 0.120(0‘)], and the contribution from EY2276 KeV

was taken into account in the gamma-fraction of E :29? Kev.

Y

b) ‘_7_Q. As shown in Figure IV.4.2b, 3 bound excited states decay by
the emission of gamma-rays. There are a number of excited states above
the neutron-threshold energy, H.1N36 MeV, which decay partially by
gamma-ray emission; however the gamma-widths of those states were much

smaller than the decay-widths (smaller than 11) [A386, $1086]. Only

EY=871 Kev was in the detection range of the NaI(Tl) detectors.

c) ”O. A number of levels above the alpha—particle threshold energy,

6.2279 MeV, still decay in full by gamma emission [A183]. Only the

IV-105
state of 7.117 MeV (H+) among those which decay partially through gamma-
ray emission has a comparable gamma-width to the particle decay-width
(FY/ra=0.9:0.1) [A383]. Contamination from EY=1650 Kev [3.632(0“) +
1.982(2+)] to EY:1571 KeV [3.553(4+) + 1.982(2+)] and that fr00111Y21937
KeV [3.919(2+) + 1.982(2+)] to EY:1982 KeV [1.982(2+) + O(O+)] was taken

into account in the determination of the gamma-fractions.

d) ‘9F. Excited states up to E:u.6u8 MeV decay in full by the emission

of gamma-rays. The alpha-particle threshold energy is “.0138 MeV

LAJ83]. uamma—decays from the states above “.648 MeV are negligible,

and a gamma-fraction.fim¢E3:1236 keV [1.346(g ) + 0.110(% )] was

Y

determined in this nucleus.

e) :jflg. A number of excited states above the alpha-particle threshold
energy, l1.7309 MeV [Aj83], decay in full via gamma-ray emission. There
are also a number of unbound excited states which decay partially into
lower states through gamma-ray emission, however only the state of

5.621(3-) has a comparable ratio of P /Pz7 1. The transition from

Y
1.63u(2+) to O(O+) is the most prominent one in this nucleus. The
uncertainty in the spin assignments for those states which decay through
gamma-ray emission becomes a problem for this nucleus and the heavier
ones. However for this nucleus the only states with uncertain spin
assignments are 10.69, 11.53, and 11.56 MeV [AJ83], and therefore the

error caused from the uncertain spin assignments would be negligible as

compared to the statistical uncertainty.

1V-106

+ +

f) 2‘Ne. Gamma-rays of EY:351 KeV [0.351(3 ) + O(% H, 1120 KeV

+ + + +

[2.866% ) » 1.7116(-;_- )1, and 1395 Kev 11.7116“; ) + 0.351(3)] are
detected in coincidence with fragments of this nucleus. Gamma—branching
ratios of excited states below the neutron-threshold energy, 6.76 MeV,
are relatively well known, however the spin assignment for many of those
states is given as a range of possibilities [En78, Na81]. In such a

case, a median value of the spins was used in the calculation of the

pred icted gama-fraction .

g) 2313. The spin of each state below 7.11 MeV is well known
experimentally, while the alpha-particle threshold energy is 9.67 MeV
[En78]. For the states, for which the spins are completely unknown, a
spin assignment for each state was made by assuming an E1 or M1
transition. Although the application of the new temperature measurement
to this nucleus and the heavier ones is less plausible because of the
limited information about the spin assignments for the high-excited
states, one must note that the feeding from those highly excited states
would not be as important as that from relatively low-lying excited
states if the population of each state was distributed according to Eq.
IV.1, and the temperature is close to the predicted value (~3 MeV).
This means that the uncertainty arising from the poorly known spin
assignments for the high-lying states may not bring a major shift in the
predicted gamma-fraction. Hence the comparison of gamma-fractions
between the measured and the predicted still remains an interesting
topic. A prominent peak of EY=1275 Kev [1.275(2+) + O(O+)] was observed

in this case.

IV—107

+ +
h) “Na. Each gamma-fraction for EYleO KeV [0.4110(3 ) ~> 00:23— )], 628

+ + +
9

+
Kev [2.7011(5 ) + 2.076% )1, and 1636 KeV [2.076% ) + 0.110% )1 was

compared to that predicted by the Fermi gas model. (kwmamination of

+

EY=177N KeV [3.850(37) + 2.076(%-)] was taken into consideratixni. The
proton-threshold energy is 8.79 MeV [En78], and even though the gama-
branching ratio of each bound state is reasonably well known, the
situation in the level information regarding the spin assignments is no
better than that for 22Ne [V084, En78], which may imply a larger
uncertainty in the determination of the predicted gamma-fraction and the
temperature. Statistics at E/Az8 MeV were not sufficient,znui those at

E/A=10 MeV were limited to only two peaks.

Gamma-rays.h12°F (656, 823, and 1001 KeV) were not included in
this analysis because of the small amount of information known about the
states [F085, Aj83, B175]. The temperatures deduced from the
intermediate fragments are displayed in Figures IV.4.3(a-c) for each
beam energy. For a nucleus with more than one gamma-ray peak, the
temperature from the lowest energy gamma—line is drawn in the left side,
that from the highest one is in right side, and so on. Since the gamma-
fracticni for this mass region is, in general, not very sensitive to the
change in temperature as shown Figures IV.11.2(a-h), the statistical
uncertainty due to the number of counts for each peak becomes
exaggerated when the temperature is around one MeV. This leads to un
upper limit of the temperature for some nuclei extending to infinity.
Table IV.4.1 shows the tabulated values for Figures IV.H.2(a-h) and

IV.N.3(a-c).

IV-108

 

IIITIII

 

 

 

 

 

 

E/A=82MeV

 

 

 

10—1 1 1 1 1 l i. 1 l
16N 170 180 19F ZONe ZlNe ZZNe 23Na

Figure IV.A.3 The observed temperatures from the Y-ray transitions of
the intermediate fragments. Dashed line represents the predicted
temperature in the Fermi gas model. a) At E/A:8 MeV.

IV—109

 

101 _

—----—---

100 T +

IcT (MeV)

 

 

 

 

 

"""""""" 1F
1 + * + o ‘3

 

 

 

 

_ + 133/A: 10 MeV 4
10—1 1 1 1 1 1 1 1 1
16N 170 180 19F ZONe ZlNe 22Ne 23Na

Figure IV.A.3 (cont'd.) b) At E/A=1O MeV.

10"1

Figure IV.A.3

IV-110

 

 

 

 

 

 

_ 0 a
o
__ o b ._
E + ’ 3
C o 2
_ E/A=12 MeV ‘
.1 1 11 1 1 1 1 1

1

1

111 11111]

 

 

MN 170 180 19F zoNe ZlNe zzNe zaNa‘

(cont'd.) c) At E/A=12 MeV.

Table IV.A.1

a) At E/Az8 MeV.

V-111

Deduced nuclear temperatures from intermediate fragments.

 

 

8)

 

 

 

E/A Isotope EY __Degay__ C NY f KT
(MeV) (KeV) (MeV)
8 ‘°N 276 0.10»0.12
+297 0.30+g.s. .551 92:23 .389:0.097 0.36:8 fig
'70 871 0.87~g.s. .221 61:26 .091:0.010 0.72:3:gg
'80 1650 3.63:1.98
+1571 3.55+1.98 .307 63:31 .371:0.183 1.2<xT<m
1937 3.92:1.98
+1982 1.98+g.s. .979 115:20 .850:0.118 1'5:0T1
19r 1236 1.35»0.11 .218 85:18 .229:0.018 3.8:2T3
2°Ne 163M 1.63»g.s. .765 78:17 -73530-160 2‘O:of9
2‘Ne 351 0.35+g.s. .711 120:35 .691:0.058 1.6:; I
1120 2.87:1.75 .116 32:11 .126:0.055 1.1:2T7
1395 1.75+0.35 .337 51:18 .218:0.088 1.1:3:fi
ZZNe 1275 1.28+g.s. .908 116:25 .750:0.162 1.2:; g
a. Predicted gamma-fraction. See the text for the detail.

V-112

Table IV.4.1 (cont'd.) b) At E/Az10 MeV.

 

 

 

 

E/A Isotope EY Decay rca) NY r KT
(MeV) (KeV) (MeV)
10 ‘°N 276 0.10+0.12
+297 0.30.3.3. 0.551 55:26 0.233:0.111 0.19:3:32
'70 871 0.87»g.s. 0.226 57:26 o.089:0.o11 0.69:8 g;
180 1650 3.63+1.98
+1571 3.55:1.98 0.311 53:15 0.330:0.093 6.2:uf8
1937 3.92:1.98
+1982 1.98+g.s. 0.986 80:18 0.626:0.111 1.0:8 i
‘9F 1236 1.35:0.11 0.222 63:20 0.153:0.019 1.2:8 g
2°06 1631 1.63+g.s. 0.771 82:22 0.315:0.092 0.71fg:}%
"Ne 351 0.35:3.3. 0.718 656:73 0.519:0.061 0.78:3 i:

1120 2.87+1.75 0.119 57:20 0.113:0.010 2.5:,“1

1395 1'75’0'35 0-3”“ 155123 0.38210.069 12.1:16 0
221118 1275 1.28+g.S. 0.913 185130 0.58510.095 0.86:g.:E
2’Na 110 0.11»g.s. 0.651 295:29 0.721:0.071 3.2mmon

+00

628 2.70.2.08 0.086 34:13 0.106:0.090 25.5_23 7

 

a) Predicted gamma-fraction. See the text for the detail.

Table IV.M.1 (cont'd.)

V-113

c) At E/Az12 MeV.

 

 

 

 

 

 

E/A Isotope BY Decay f0 NY r KT
(MeV) (KeV) (MeV)
12 '61 276 0.10+0.12
+297 0.30+g.s. .556 268:70 .370:0.096 0.33:8 i?
'70 871 0.87+g.s. .230 175:13 .085:0.020 0.66:8::g
'80 1650 3.63+1.98
+1571 3.55+1 98 .316 172:13 .293:0.073 2.2:;.9
1937 3.92.1 98
1937 3.92+1.98
+1982 1.98+g.s. .991 311:33 .665:0.071 1.1:0.1
"F 1236 1.35:0.11 .226 277:68 .186:0.015 1.6:g:;
2°16 1631 1.63+g.s. .776 122:16 .137:o.o18 0.81:3 33
2‘Ne 351 0.35+g.s. .753 2917199 .561:0.019 0.82:0.07
1120 2.87»1.75 .122 231:50 .107:0.023 2.2:3 g
1395 1.75:0.35 .350 513:50 .308:0.028 2.0:3:;
=2Ne 1275 1.28+g.s. .918 980:73 .709:0.053 1.1:3 f
230a 110 0.11.3.3. .651 2130:90 .637:o.021 2.3:3 ;
628 2.70:2.08 .088 219:17 .083:0.016 2.8:g:;
1771 3.85+2.08
+1636 2.08+0.11 .297 337:55 .258:0.12 1.7:3 g
a) Predicted gamma-fraction. See the text for the detail.

IV-1111

The overall result shows that the observed gamma-fractions at E/A:8
MeV are, in most cases, larger than those at E/A:10 and 12 MeV. The low
gamma-fractions observed at E/A=10 MeV are somewhat contradictory to the
result from light fragments, while the lower values at E/Az12 MeV show a
consistency with the results in the preceding section. 1"N and ”0 may
be regarded as two of the best probes among those under consideration in
a study of the population distribution of intermediate fragments since
these have only three bound excited states, and the feedings from the
unbound states are experimentally well known to be negligible. However
the temperatures observed from these two nuclei are surprisingly lower
than those from the other nuclei at all the beam energies. If one
assumes that these fragments are produced from a thermally equilibrated
composite system, the lower temperature for “N and ”0 can be
explained either by the possibility that there exist a number of
experimentally unknown high-spin states which exclusively decay into the
ground state through the gamma-ray emission, or by the preferential
feeding to the ground state from the particle unbound states in higher-A
nuclei system [Ha88, Ha87, M085a, Mo8Aa, St83].

Feedings to the bound states by particle decay of higher-A nuclear
unbound states are calculated by the quantum statistical model [St83,
Ha87, Ha88] as modified by Fields et al. [F187]. In the modified
quantum statistical model, it is assumed that the primary populations
depend on the temperature, binding energies, spins, and Coulomb
barriers. Figures IV.A.N(a-b) show the comparisons between the data and
the calculated values for some of complex fragments. Solid lines
represent the gama-fractions calculated from the primary population

distribution, dashed lines show those from the modified quantum

IV-115
statistical model [Fi87]. It is shown by this model that an appreciable
effect due to the feeding from the unbound states in the higher-A
nuclear systems on the gamma-fractions exists at the temperatures
expected for the present beam energies. Especially, the much lower
gamma-fractions measured for "Li and ”Be at E/Az12 MeV may be
significantly due to this effect, as shown in Figure IV.A.Aa. According
to the model employed here, at temperatures above 2-3 MeV the gamma-
fractions for the gamma-ray transitions in 7Li and 7Be will decrease as
the temperature gets higher because of the preferential feeding to the
ground states. The lower temperatures observed in the reaction of ‘“N +
”C with E/A212 MeV [M086a] may have been due to this effect, too. For
"N, a preferential feeding to the isomeric high-spin state, 0.297(3-),
is predicted by the quantum statistical model [St83, F187], hence

leading to overall lower temperatures for this nucleus which are as yet

unexplained. For 1"0, feedings to the high-spin states, 3.8111(3- ) and

0(3 ), are predicted to be much larger than those to the low spin

states, 3.055(%-) and 0.871(-;;), which means that the game-fraction of
EY=871 KeV transition after the preferential decays to the high-spin
states will differ significantly from that calculated from the primary
populations. This prediction agrees well with the data, which is shown
in Figure IV.A.Ab for "'0. As many more excited states get involved in
the measured and calculated gamma-fractions for fragments heavier than
”0, the preferential feedings to certain states may not play an
important role for the gamma-fraction; in other words, the gamma-

fraction predicted after the preferential decays may not be

significantly different from that calculated from the primary population

IV-116
distributions only. An example is shown in Figure IV.4.Mb for ‘30. The
calculated gamma-fractions before and after the preferential feedings
are only slightly different from each other for both EY=1982 Kev and
1571 Kev transitions in ‘50.

The quantitative discussion of the preferential-decay effect on the
final population distributions may not be feasible without more detailed
knowledge of the primary population distributions. However, since
direct measurements of the primary populations are not available, the
underlying physics of this discussion must be confined to the
qualitative predictions. The final population distributions predicted
by the modified quantum statistical model [Fi87] are compared with the
experimental data in Figure IV.14.5. The solid lines in this figure
represent the predicted cross sections at each beam energy, and these
are normalized to ”B. The results of the model are presented only up
to the oxygen isotopes, but isotopes up to A:21 were included in the
code. Since angular distributions were not obtained in the experiment,
they were calculated according to Ref. M075. The angle for the peak
velocity in the center-of—mass frame (ranging from 29° to 118°), which
was calculated by transformation of the laboratory angle with the peak
velocity, has been used in the calculation of the total cross section
for each nucleus. In Figure IV.A.S, it is shown that the prediction
reproduces the relative cross sections reasonably well over the mass
range under consideration. Lower observed cross sections for the
lithium isotopes (obtained only for E/A=8 MeV) may be due to the
uncertainty arising from punch-through problems in the detection of the
fast-moving light fragments. The agreement of the cross sections

between the experimental and that predicted for ”C implies that the

IV-117

 

Ivvvlfvvvlvvrv.

r1

 

 

_. .J
1. A «1
1- ° 4
P m I
b 0 1
— u —1
1- a
b d
: m 1 :
7' CD '7
b ' H m d
P H 1
D I 0 q
: O :
1- v ‘
— .
b 1
if I l ; t I § 4 J 1 L1 1 1 ‘
1- t 1 v I r r v t

_ 1 r l 1

1-

III

Be

7
(0.429 —» G.S.)

IIIITII

II

 

 

12C(4OAI', X)

III
«1'7"-

 

1P
lllllllllllllllljllAllll

I.
6 81012146 8 101214 6 8 101214
E/A (MeV)

IIIIIIIjIIIlIIIIIIIIIIII
All.

 

 

 

 

‘1! ('3. N. "3
o o o o

NOIiovaa—L

Figure IV.4.“ Y-fractions after the preferential feedings from heavier
nuclei (dashed lines). The data points and the solid lines are same as
in Figures IV.3.2 and IV.A.2. a) For light fragments.

IV—118

gas; «\m

vfimdoam ovfimficfim owfimficfim m

—¢d-1—q1q<—1<u4—quu—qq< 1—1-11—4-14—1d1d—14d—d 1 q—j4d 1—0144—«11:—j—

 

“ .. H 36 1 Emma

» 11111 1 ..
. 48 o .. + r .. 22 U
. + : III/I : O a

I JV 4

 

 

 

 

 

 

 

. m2: .. «new 0 + .. .
. .m.o .. News 0 .. émd 1 3.98 1111111 11111.11

:8de... 3794.... .1
.1

 

1.-

I
bP—PhhP—bhbb_bbbD—bbbb1_ybb

 

 

 

 

Pl—Prrb-Ph-b—PDDP—Dbbbph

 

CA #19358

b) For intermediate fragments.

NOIiovaa—A

Figure IV.A.A (cont'd.)

102

101

(arbitrary units)

0'

Figure IV.A.S

IV-119

 

 

' E/A=12 MeV 1*
1' :
1 1:1 1:1 1
E- D D D D D D a?
13
l l l l l l l l l l l l l l l J l I l l l
1 E/A=10 MeV 1
1' .
E I
E" D D D D :1 0 CF
' D D U .

 

 

 

 

 

Cross sections for complex fragments. Solid lines

represent the predicted cross sections by the quantum statistical model

[St83, F186] .

IV-120
contribution from the target-like moving source [Ch86a, Ch87a, Ch87b] is
not important in the formation of fragments in this mass region for the
present reaction.

In conclusion, the observed population distributions of the nuclear
states in the light fragmentation region (Li, Be, and B) at E/A=8 and 10
MeV are in a rough agreement with the predicted values under the
assumption of the simple thermal equilibrium, which indicates little
effect of the preferential feedings from the higher-A nuclear unbound
states on the population distributions at these low bombarding energies.
However, the data for the light fragments at E/A=12 MeV and those for
the intermediate fragments at all the energies show fluctuations in the
observed temperatures. This can be interpreted to mean that the
variable feedings from the higher-A nuclear systems play an important
role in the formation of the nuclear states along with the primary
population of each nuclear state, however the data shows also that the
quantum statistical model may have overestimated the the feedings for
certain states in certain nuclei. The variation in the feeding from one
type of fragment to another must depend on the nuclear structure
characteristic of the higher-A nuclei especially for the very high-lying
unbound states. This ought to be also associated with the temperature
and the decay channel of the composite system [8083, St83, 3081}, M085,
F187, Ha87, Ha88]. Hence this leads to the idea that the low
temperatures observed for "Li and 7Be at E/A212 MeV may not imply the
failure of equilibrium at this beam energy. A calculation with the
quantum statistical model [Ha88, Ha87, F187, St83] supports this
statement qualitatively by explaining that the lower temperatures than

those predicted for some nuclei, for example, ”0, may be due to the

IV-121
significant amount of preferential feeding to the ground state. In no
beam energy for this mass region, there was any indication of the yrast-
line dominant gamma-ray emission, which is most common in the residual
heavy fragments. An indication of consistency with thermal
equilibration at E/A212 MeV is somewhat different from the result in
Ref. M086a, however this may be studied further by increasing the
bombarding energy and also observing the gamma-transitions from the
higher-lying states. As a reliable prediction of the primary population
is an essential factor in the quantum statistical model [St83, F187], a
more realistic formulation is required in the calculation of the primary
population distributions, for example, the inclusion of the fission-
fragment yield dependence on the maximum angular momentum of the

compound nucleus [808“].

IV.5 Errors

The errors involved in the evaluation of the gamma-fractions (or
temperatures) are due to statistical uncertainties and systematic
errors. The systematic errors are primarily due to the uncertainty in
determining the gamma-ray detector efficiency, which are estimated in
total to be about 5% for NaI(Tl) scintillation detectors and 21 for Ge
counters. The statistical uncertainties are due to the least-square
fitting procedure of a Gaussian function plus background. A typical
example of the fitting is shown in Figure IV.5.1 for the case of 2°Ne.
The solid lines represent the Gaussian-function fittings with the
backgrounds, which were fitted by a second order polynomial function.

Errors evaluated by this procedure turned out to be larger than, or

IV-122
comparable to, those calculated by the standard way according to

Myzmy+2NB' where N is the number of counts in the peak area with the

Y

background subtracted and N is the summed area of the background (area

B
between the dashed lines in Figure IV.5.1). Possible errors for gamma-
rays emitted from the long-lived states must be taken into account
because of the effect on the geometrical efficiency and the Doppler
broadening. For example, an error of 10% was estimated for the gamma-
ray of 718 KeV for ‘°B.

The net error in determining the number of counts for each ganma-
ray peak was obtained by taking the square-root of the sum of the
squares of the individual errors. This gives the results shown in
Tables IV.3.1 and IV.M.1. As the statistics are limited substantially

at E/Az8 and 10 MeV for the intermediate fragments, the statistical

errors dominate the net errors in those cases.

IV-123

 

 

 

 

125 ' " " " r' " " '
.
100.-
D
755-
I
505'
D

‘ E A=12 M V

25.- / e I

I I

D ‘

() : : iifir f*:. e t .: % cs : - c,

.2

 

 

 

 

E/A=10 MeV .

() ’. . . l 1 - . L,.. L . i . Li 1, . . . .

, ' ' ' ' I ' ' ‘ ' I f ' ' 1' I ' ' ' '
r 1

 

 

 

 

 

COUNTS PER CHANNEL

E/A=8 MeV
60 so 100 120

CHANNEL

Figure IV.5.1 An example of the Y-ray peak fittings for 2“Ne. See the
text for detail.

CHAPTER V: POPULATION DISTRIBUTION II

(HEAVY RESIDUAL FRAGMENTS)

V.1 Introduction

Continuum gamma-rays with high multiplicities have been observed
previously in heavy-ion reactions [e.g., Ne77, Ha75, 8176, N675]. A
study of the energy spectra [Ne77] of these gamma-rays showed that the
multiplicity spectra have peaks at energies around 1-3 MeV, and these
gamma-rays have been interpreted to be associated with the "yrast and
statistical cascade" [Ne77].

It is well known that, in reactions well above the Coulomb barrier,
the compound nucleus is formed with relatively high angular momentum and
high excitation energy. The overall decay of this excited compound
nucleus includes strong contributions from the emission of light
particles, such as neutron, proton, and alpha-particle emission, and
fission competition becomes important for the decay of the compound
nucleus with high angular momentum. However, since light particle
evaporation removes a relatively small amount of angular momentum, the
decay of the composite system is heavily influenced by the yrast line.
The emission of light particles will, in general, continue until the
system eventually cools down to the point at which gamna-ray emission
starts. The primary population distributions of nuclear states in the

heavy residual fragment region, therefore, may be governed by the

V424

V-125

maximum angular momentum involved in the entrance channel, fission of
the compound nucleus to produce sizable complex fragments, and the
competition between light particle evaporation and gamma-ray emission.

Information about the population distributions of the bound states
can be obtained from gamma—ray emission, as shown Ch. 1W]. Under the
assumptixnicof complete fusion, the emission of gamma-rays observed in
coincidence with the heavy residual fragments should reflect the
dependence on the statistical decay-chain which is associated with the
excitation energy and spin, the shape of the yrast line, auui the
dinuclear dynamics in the entrance channel; but not on the Boltzmann
distribution which prevails apparently in the production of complex
.fragnun1ts. It is, therefore, interesting to compare the experimentally
observed intensity of gamma-rays from the heaviest fragments wiini those
predicted by the statistical model [P077] in order to study a
fundamental aspect of the formation of the composite system.

In the present reaction, if a compound nucleus was formed, the
excitation energy would be about 92 MeV at E/A:8 MeV, 113 MeV at E/A:J()
MeV, and 131 MeV at E/Az12 MeV. These values are sufficient to
evaporate a number of nucleons or alpha-particles, and as a consequence,
the residual fragments will be deflected from the original beam
direction due to the recoil of the emitted particles. Hence, by
employing reverse kinematics, which provides a large laboratory energy
for the center-of—mass frame, and by placing the particle detectors at
small angles relative to the beam direction, the evaporation residues
can be detected. This also enables the measurement of gamma-ray
(unission in coincidence with these fragments, and therefore the

population distribution of the particle-stable-excited states. Although

V-126

the individual isotope separation:nsrmm.available, the clear 2-
identificathmmcfl‘the heavy residual fragments in the particle
telescopes, which is shown in Figures III.1.3(a—c), is essential for

this measurement.
v.2 Statistical Model

The CASCADE nuclear evaporation code [P077], as modified by Harakeh
for low energy heavy-ion reactions, predicts the population distribution
of the evaporation residues, and is based on the statistical theory fin“
compound-nucleus reactions (Hauser-Feshbach theory). This model assumes
that projectile and target form a compound nucleus in statistical
equilibrium, and then the compound nucleus decays by emission of light
particles (alpha-particle, proton, or neutron). Hauser-Feshbach
formulas are applied in this model in order to calculate the intensities
of the various decay modes of the compound nucleus. Fission has been
neglected in the decay mode of the compound nucleus in this model,
however an effort to take it into account is made by cutting off the
highest partial waves in the compound nucleus. No estimation for pre-
equilibrium emission is made in this model.

Following Ref. Pu77, the cross section for the formation of the
compound nuclei from projectile and target nuclei with zero spin and
even parity for both, which is relevant to the present reaction, is

given by

oCN « X (22+1) TQ(E) . (v.1)
Q,“

V-127

where 2 represents the spin of the compound nucleus, and E is a center-
of-mass energy. The summation over spin 2 is restricted by the parity

selection rule n : nPnT(-1)Q : (-1)Q, where n and n“ represent parities

P l

for projectile and target nucleus, respectively. The transmission

coefficients TQ(E) are approximated by a Fermi distribution [Pu77]

1
2 ‘ 1 + exp[(Q—Qo)/d] '

 

(v.2)

where 2, corresponds to the critical or maximum angular momentum for
fusion, buiichever is smaller, and the diffuseness d is responsible for
cutting off a portion of the highest partial waves.

The decay width for emitting a particle x from an excited nucleus
of excitation energy E,, spin J,, and parity n, to form a product
nucleus of E,, J,, and n, is given by [P077]

J2+s

[1t]
_ QAEZIJZJH'L) x
fx(ex)

X
‘ 2np.<E..J.,n.> TL(€x’ ’ (“‘3’

S:[J2-sx[ L:[J,-S[

where ex represents the kinetic energy of particle x (equal to EVE,-
separation energy), pi (i=1,2) is the level density, 3x and L are the
spin and the orbital angular momentum of particle x, respectively, and
the channel spin 8 = Jz+sx. Again, the sunmation over L is limited by
the parity selection rule, and the transmission coefficients T: are
obtained from the optical model.

An analytical form of the Fermi gas level density is applied in the

very high excitation energy region (liquid-drop region), innile in the

low energy region, either the experimentally known levels or the

V-128

analytical formulas can be used. The yrast line is calculated as [P077]

J(J+1)h2

E (J) : 21

rot + A , (V.u)

where Ixmmwesents the moment of inertia, and A is a pairing energy
which determines the zero point of the effective excitation energy. The
appropriate input of the moment of inertia comprises a crucial gnaint of‘
the calculation for the population near the yrast line. A careful study
of the experimentally known high-spin states was carried out in the
current calculation to obtain a proper shape of the yrast line for each
nucleus. The density parameter (a), pairing energy (A) in Eq. V311, and
tin; fraction of the moment of inertia relative to the rigid body (I/Io)
used as Unainput parameters for the calculation are given in Table
V.2.1.

In the evaluation of the gamma-ray intensities, the experimentally'
known level information, including the ganIna-branching ratios, has been
used for the low-lying states. For the very high-lying states about
bfl1ich little is known, the model calculates the gamma-decay rate
RYde:Y from a state (excitation E,, spin J,, parity 1:.) to another state

(E2, J2, n2) according to a formula [P077],

_ 9(E22J21flz)
rY(eY) - 2flp(E"J"fl1) E gLfL(eY) , (v.5)

wherwa‘J represent the density of states, L denotes the multipolarity of
the ganma-ray, and gLfL(€Y) are energy dependent strengths. Only E1,

M1, and E2 transitions are considered in this model.

V-129

The maximum angular momentum Qmaxz39 h, which is obtained with rmax
.: 1.2(A1/3+A21’T3) fm, is used in the CASCADE code calculation in order
to reproduce the mass distribution spectra better than with ch=32 h
“d180, M086b]. Although the proper use of the maximum angular momentum
is critical in the mass distribution spectra, it was found that the
relative gamma-ray intensities for the transition along near the yrast
line are not very sensitive to Qmax' As a matter of fact, it was found
that the broad shape of the predicted primary population distribution
(kn-the relative population densities of nuclear states) in a spin-
excitation energy space depends mainly on the function of the excitation
energy range in the decay array, even though the yrast line
concentration prevails in most cases. A couple of examples of the
calculation are shown in Figures V.2.1(a-b) for ”Ca and 3"Ar. Thick
solid line represents the yrast line. Competition between nucleons,
alpha-particle, and gamma-ray are also shown in the figures (upper
dotted line denote partial nucleon decay width of 50% and lower line

denote partial gamma-ray decay width of 50%). Thin solid lines drawn in

the figures represent the shape of the primary population distributions.

mb
MeVoh’

divide the spin-excitation energy space into the gamma-ray decaying

 

The unit used in the population-density grid is Dotted lines
region, alpha-particle decaying region, and nucleon decaying region
according to the decay probabilities as in Eqs. V.3 and v.5. Yrast-line
dominance in the population distribution can be seen in the figure for
both the nuclei. However, one should note that the population along the
yrast line is rather sensitive to the moment of inertia, as mentioned

earlier.

V-13O

Input parameters for CASCADE calculation

Table V.2.1

 

 

 

 

Mass

Charge

11111 1.1.1.1.1.nunvnvnvnv1.1.nvnv1.1.nv1.nv9.1.nonoQJnv1.nunununonunvanunununununuou
111111111111 1111111111111111 01100110101000000

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Table V.2.1 (cont'd.)

V—131

 

Charge

18
17
17
17
17
16
16
16
16
16
15
15
15
14
1”

 

\DOOOGQQOQGDOQGJGDO

.52
.70
.86
.03
.02
.86
.03
.02
.01
.01
.02
.01
.01
.01
.00

 

-0
-1
—1
-1
-1
-2
-1

-2
-1

.55
.99
-2.
.06
-2.
.0“
.57
.08
.10
.10
.U2
.10
.45
.11
.23

39

OOOOOOOOOOOOOOO

L:

 

V-132

12C(4°Ar,2a2n7)42Ca, E/A=8 MeV

I f I V V V V l V V V V I Y V V V i 1 f V 1 I "

 

(I‘N+I‘,)/I‘ > 0.5

so - . .-

20 P ~a=§ lmb

E“ (MeV)

1()" ........ "".. n
. lf 7 0'6 a= 10mb

 

 

 

o AAAAJ LALLIALAAIIALAIAAALIL

O 5 10 15 20 25

Figure V.2.1 Predicted primary population density distribution by the
CASCADE code [P077]. See the text for detail. a) For “’Ca.

V-133

12C(40Ar,30<2n7)38Ar, E/A=8 MeV

 

 

 

 

 

_ I . . - . I . . . . I . r ,
20 - (rn+r,)/r > 0.5 049 -
. 1 .
AS
' a
g F .' -1
15 - —
Q) . .1
2 P a= 0.01.1nb ‘
=11: .
= lmb _
Efl
= 10mb -
O l l L i l L 4 i . L . L i i L . l
0 5 10 15

J (h)

Figure V.3.1 (cont'd.) b) For 3"Ar.

V-13’4

V.3 Population of Nuclear States

Figures from V.3.1 to V.3.7 show the Doppler shift corrected gamma-
ray spectra.for the Ge counters in coincidence with isotopes of Ti, Sc,
Ca, K, Ar, Cl, and 3, respectively, at E/A:8 MeV. Gamma-ray peaks with
sufficient statistics are labeled with their energies in units of Kev in
these figures, where the number before the colon(:) in each label
represents the mass number. Statistics at E/Az10 and 12 MeV are limited
because of the limited energy range set in the AzE-silicon detector.
The identification of the gamma-ray peaks was carried out in a manner
which was based on the experimentally known spin and excitation energy
of each state and the gamma-branching ratios. Even though broad
features of the gamma-ray peaks can be obtained with the NaI(Tl)
scintillation detectors [Figures V.3.8(a-c) are shown as an example for
K at each beam enerSY], one can use only the Ge counters to determine
the separate gamma—ray intensities. Peaks at low gamma-ray energy
appeared with a relatively good resolution, however the Doppler
broadening which mainly comes from the finite geometrical shape of the
gamma-ray detectors have widened the widths of peaks at higher gamma-ray
energies, which makes the separation of the closely located gamma-ray
peaks difficult or impossible.

Tables from V.3.1 to V.3.7 show the observed gamma-ray intensities
(IY) at E/A=8 MeV/A. Comparison with those predicted by either the
CASCADE code [P077], which is described in the following section, and/or
the Boltzmann thermal distribution with a temperature of KT=2.76 MeV,
whitni is calculated for E/A:8 MeV by the Fermi gas model, is also given

in the tables. The calculation of the Boltzmann distribution was

V-135

carried out for some of the less heavy fragments (e.g.,EL Cl), for
which the statistical model [P077] predicts little populatitnus, and it
was done only for those nuclei which have relatively well known level
information. Errors included in these tables represent the statistical
uncertainties which are due to the least-square fitting procedure of the
Gaussian function plus background, as discussed in Sec. 1V.5. Since the
total cross section of each 2 is not available for the heavy residual
fragments in the present experiment, and since the limited energy range
also disables the determination of the relative population ratios
between isotopes by means of the gamma-ray intensities (because the
energy range for each isotope’with the same 2 will differ), the
comparison of the observed cross sections with those predicted is not
practical for these fragments. A future experiment designed
specifically for heavy fragments would be very useful.

The observed strong transitions for each isotope are described in

the following subsections:
V.3.1 Titanium (Ti)

The strongest gamma transition for 2:22 in the present reactitni is

along 6.214(10”) + 11.9O(8+) . 3.30(6+) » 2.0mm“) + 0.89(2*) ~ 0(0“)
. , . 17‘ 15‘
[Ra82, P081] with “ T1. Gamma-rays along 3.60(-§ + 3.02(-§- +
ll- 1. .5.- .3.- .3.-
1.147( 2 ) * 0(2 ) [F078] and 0.71102 ) + 0.33(2 ) -> 0.0M2 ) [K3811] are
observed with “5T1. Some of the low—lying transitions in ““Ti and ““Ti

[Wa86a] can be also seen in Figure V.3.1, however the statistics are

limited.

V-136

'Dable V.3.1 shows the observed gamma-ray intensities in “5Ti and
“Ti, respectively, at E/A=8 MeV. According the CASCADE calculation
[P077], most of the bound states in “Ti are produced by decays of two
protons and four neutrons (2PAN) from the compound nucleus, 52Cr, bfliile
the residual fragments of HTi are formed through decays of an alpha-
particle and three neutrons (aBN). Since the excitation-energy range of
tine primary population of “°Ti extends only over the low energy region,
the gamma-ray transitions between high-spin states depends mainly on the
shape of the yrast line. On the other hand, the primary population
distribution of “5T1 will be scattered widely over the excitation energy
regitnl, which means that the gamma-ray intensities are sensitive to the
shape of the yrast line. This is supported by the observed data; the
gamma-ray intensities along the yrast line in ”Ti are roughly constant
(high-spin states above 5.42 MeV are not well known experimentally
[Ka8u1), while the transition of 6.2u(1o*) » A.90(8+) is apparently

weaker than those between low-lying states.
V.3.2 Scandium (Sc)

Transitions of 3.570?) + 2.67(9+) + o.97(7*) + O.27(6+) in “So

[En78] and 3.694%.) + 2.110%.) + 1.211(l-g) + mg.) in ”So [Le78] are
observed. The state of 0.27(6*) MeV in “"Sc is an isomeric state with
11/2=2.1111 days, hence the transition of this state to the ground state
could not be observed in the present experiment.

Fragments of ”Sc are predicted to be produced by decays of aP2N

from the compound nucleus and “So by decays of aP3N according to the

V-137

statistical model [P077]. The excitation range for both the nuclei
extends over from the low energy to the intermediate energy region. The
observed gamma-ray intensities for these nuclei are shown in Table
V.3.2. Data for ”So indicate a fair agreement with the prediction,

although the prediction shows no enhancement for the population of the

1.2“ (1%5) MeV state while a larger population of this state or-zi large
feeding to this state from states inside the yrast line is indicated by
the data. The isomeric (or high-spin) character of the 3.57(11+) MeV
state in “Sc leads to the prediction of a large population for this
state. Although the uncertain spin assignments for the 11.11 and 3.98
MeV states limit the comparison to only the knwdying transitions, a
rough agreement between the predicted and the observed gamma-ray

intensities is provided for ““Sc.
V.3.3 Calcium (Ca)

The strongest transition line of those observed for 2:20 is along
7.75(11')+ 7.37(1o‘) » 6.55(9‘) + 5.711(7’) ~> n.10(5‘) + 3.19(6+) +
2.75M’) + 1.52(2*) + em”) in ”Ca [En78, Eg78b, Ke80, He81]. A

sequence of the E2 transitions along 11.72(6+) + 3.25(11+) + 1.52(2+) is
. . . 15' 11‘
also observed with (.a. The tranSltlon of 2.75(—§ * 1.68(—‘2 ) +

0(‘3‘ ) is the main one in ”Ca and also that along 5.930% ) -9 5.16(-1-%

+ 439(33- ) [En78, Be78, Be79] which flows down inside the yrast line is
observed.
The observed gamma-ray intensities for ”Ca and ”Ca are compared

with those predicted by the CASCADE code in Table V.3.3. Data for ”Ca

V-138

and ”Ca show a major disagreement with the CASCADE code prediction for
the transitions between states inside the yrast line, for example,
EY=776 and 761 KeV in ”Ca and EY:11162 and 1729 Kev in ”Ca. The
observed gamma-ray intensities for these transitions are comparable to
those for yrast line transitions, while the predicted values are nearly
negligible compared to the latter. It is also obvious that the model
fails to predict the relative populations for the yrast-line states,
especially in the low-lying transitions in ”Ca. The model predicts
larger populations than observed for the high-lying states, or smaller
populations for the low-lying states. One has to remember that both the
predicted and the observed gamma-ray intensities are normalized to a
certain transition, hence the terms "larger" and "smaller" are relative.

Gamma-ray intensities under the assumption of a Boltzmann thermal
distribution with xT=2.76 MeV are calculated by virtue of the relatively
well known level information and compared with those observed for “’Ca

in Table V.3.3. Since the 3.19 MeV is a long-lived state with 1' =5.”

1/2
ns, a substantial decrease in the observed ganma-ray intensities from
decay of that state is expected. Nevertheless, the Boltzmann
distribution calculation predicts smaller populations than those
observed for the high-lying states, and larger populations for the low-
lying states. A rough agreement for the transitions inside the yrast
line is quite remarkable. These results seem to show that statistical
emission is still an important process in the population of this
nucleus, however there exists a possibility that a Boltzmann

distribution may also play an important role in the population of the

low-lying states.

1.1-139

V.3.N Potassium (K)

Gamma-rays along 2.511(7+) + 0.89(5—) * 0(14_) [En78] are observed

with ”K. “‘K have two strong transition lines; 11.99(% ) .. 11.28(1—g s

+ + +

- - +
2.764% ) -> 1.290;- ) and 3.9001; ) + 2.770% ) + 2.53(l% ) * 1.680% ) *

...
0(% ) [En78, Eg78a, Li78, St86]. The transition of the 1.29 MeV state
to the ground state could not be observed because of the long half-life

of =7.2 ns. The transition of A.60(9) » 3.56(8) + 1.95(7+) +

11/2
1.38(6+) - 0.6705-) + 0.26(‘4_) * 0.11(3-) + 0(2-) [En78, Wa75] is the
strongest one for “2K.

Fragments of these isotopes are at least three light particles less
than the compound nucleus. For ”K, decay of 2a1P3N from the compound
nucleus of 52Cr with the excitation energy 92 MeV will cool down the
residual fragment significantly. The predicted excitation energy range
of the primary population distribution for ”K is from 0 to 8 MeV only,
which means that the population of fragments for this nucleus will be
concentrated in the very low-lying states. However the observed gamma-
ray intensities for ”K, which are given in Table 11.3.11 along for “K
and ”K, show that the CASCADE prediction underestimates substantially
the populations at high excitation energy region in ”K. This can be
interpreted to mean that the evaporation process of the compound nucleus
may not be the main exit channel to produce ”K. In Table V.3.ll, one
may also note that the CASCADE calculation overestimates the population
of high-lying states and underestimates it for states inside the yrast
line for the case of “K. Data for ”K show a rough agreement, however

the long half-life, T =1.1 ns, of the 0.68 MeV state complicates the

1/2

V-1NO

overall comparison for this nucleus.
V.3.5 Argon (Ar)

Gamma-rays along 6.A1(6+) * A.59(5-) + 9.48(A-) * 3.81(3-) +3

2.17(2+) + 0(0+) [En78, Aa79] in 36Ar are from the nain transition,
. ,, . . 17" 15+
while Ar also had a strong tran31tlon of 5.55(—§ ) + H.5N(—§ ) »

3.99(l%+) + 2.65(l%-) + 0(%-) [En78, Ha87]. Gamma-rays in “°Ar are
relatively weak (EYz1u61 Kev will be the strongest transition for “‘Ar),
and this indicates that the quasi-elastic scattering of the projectile
(“°Ar) is not an important process in the production of these fragments.

Data for 38Ar and 39Ar are given in Table V.3.5. Level information
including spin, energy, and gamma-branching ratio of each state is
relatively well known for 3"Ar, which encourages a thermal calculation
for gamma-ray intensities. The rough agreement between the prediction
of the CASCADE code and the observations for 3"Ar is somewhat
surprising, while the thermal calculation with the Boltzmann
distribution overestimates the populations at knrdying states. For
39Ar, the statistical prediction overestimates the populatixni<3f high-

lying states.
V.3.6 Chlorine (Cl)

Transitions along 2.52(5-) + 0.79(3+) * 0(2+)1U13°Cl [En78] and

those along 5.274% ) + u.55(1% ) . thong ) . 3.1m; ) + or;- ) in “c1

[En78] are observed. Also, gamma-ray of 638 Kev [1.31(11-) + O.67(5-)]

v—m
and 755 KeV [0.76(3’) . 0(2‘)] were observed with ”Cl, while the

isomeric state, 0.67 MeV, has the half—life, T =715 ms [En78].

1/2

Since the CASCADE calculation predicts little cross section for the
nucleus with charge equal to 17 or smaller while the experimental cross
sections for those nuclei are comparable to 2:18, 19, or 20, a
comparison of it with the observed values becomes less plausible. In
particular, the negligible cross section predicted by the model for 36C1
disagrees with the data directly, and this encourages a calculation of
the thermal population distribution. This could be done because of the
large amount of information on the levels and ganma-branching ratios
that exist for this nucleus. The calculated gamma-ray intensities from
the CASCADE code are compared with those observed for HCl. The results
are shown in Table V.3.6. The same argument made for ”Ca can be
applied to these nuclei; there is an overestimation of the populations

at high-lying states by the CASCADE code calculation and an

underestimation by the Boltzmann thermal calculation.

V.3.7 Sulfur (S)

+ 1+

Transitions of 1.9702- ) + 0(%+) and 0.811(-2- ) + 0(%+) are observed
with 33S [En78, Ra85]. 5.69(5-) .. l1.6.2(3.) * 3.30(2+) «r 2.13(2+) *
0(0+) in 3“S [En78, Ra85] is the strongest gauma-ray sequence in this
isotope.

Table V.3.7 shows results for 33S and 3"S. A comparison with the
thermal calculation is carried out for both nuclei in this table. Even

though there exist uncertainties which arise from the limited level

1.1-1112

 

120 (40Ar, 7T1), E/A-—-8 MeV

 

 

 

 

 

 

 

 

 

 

80
:r E 3 3 13°
i~' ff ‘3' s a ‘
so; ' a 9 2 Z 2 I
9 ‘1
Z 3‘ '10
<13
m: i
O ll...l.L..J.... is] i . i l l l . l . L. O
\ so 100 150 200
U) a,
E-1 E. g
Z s " § ‘3
D i if ‘9‘
o “i '3
U
0 . . L L . . i l .
250 300 350

 

CHANNEL

Figure V.3.1 Doppler-shift corrected Y-ray energy spectra (Ge) in
coincidence with Titanium (Ti).

V—1113

12C (40Ar, 780), E/A=8 MeV

 

 

 

 

 

100’
[s
so 'I §. § § 3;
: 3 .. r. -- 3 :9 8
so 3 Q o
1-—.] $ -- ..
m 6°? 3 3
Z i
2 4°?
a
O 0 i l l l L . l i . l L l i i l i l i
\ 507 100 150 200 250
40— '3
z r “i
I 8 3
D 307 ,“3 3
O : 9 i
o 201' I l
10:—
0 ’. . LL,l . Ll . L, 1 . L, . . 1 . . . l, 1 .
300 350 400 450

CHANNEL

Figure V.3.2 Same as in Figure V.3.1 with Scandium (Sc).

12C (4OAI‘, 7Ca),

1.1-1‘11]

E /A=8 MeV

 

 

 

 

 

 

 

 

[ - 1250
N 3 o 4
3000 — § 3 333 ° 8 I
L ... ”g g + -
.. ...; .. " ... a _ 1000
S 1- 3+ 3 E E g j '
._J - a a t. 9 2 ‘
m 2000 - :2 ‘3 a} 750
z i i 8 g 3
z I g 9i 500
<3 1000 L 6, i
L in .
CI: 250
U 0 LLLLLlLLLLlLLLL Ll L L L L l L L L L l L L L L l L 0
\ _2o 40 60 80 100 150 200 250
U) : as
E“ 400E- 9 «,3
Z - s i 2
D 300 ' 7- § §
8 ..
O : ,9} 3
' 8 E 3
100:- '¢ g
l L L l L L L L l L L L L l L L L l L L A
300 350 400 450 500 550

Figure V.3.3 Same as in Figure V.3.1 with Calcium (Ca).

CHANNEL

V-11-15

120 (40Ar, 7K), E/A=8 MeV

 

 

 

 

 

 

 

500

450

400

300

 

 

m m m m o
8 6 4. 2
1 L _ 4 4 _ L 1 _ q . L 0
:3 ”3 1 %
«an ”3
So i.
0
l 0
2
2:. "me 2.8 .3+
95 ”we 82 "3
26+ one Luv L O
1 5 ms: Luv
«S ”3 L 1
«E L
So 6+ 30383 ”3
9153 "we L 0 so: ”3
l 0
1
Sn ”an on”: 6.3
w 33 .8
L...\N L
L
SN 3* ILL O
LN L 6 33:8" ”9
a
a: "av lL 0
L 4 on: a?
fur L as: "3+
2: "no 1. m «a: ”9
Lr._ ._....L+. L .LL .1..._.
0 0 0 0 0 0 O 0
0 0 O 0 0 0 0
0 0 0 0 3 2 1..
4 3 2 1

amzzsmgmszgo

350

CHANNEL

Same as in Figure Figure V.3.1 with Potassium (K).

Figure V.3.A

V-1116

120 (40Ar, 7Ar), E/A=8 MeV

 

 

 

 

 

 

 

 

 

10000 L” J 1250
3000 L” —: 1000
1—] o N R’
[fl 6000 r it 8 3 1 750
Z 5 s as;
Z 4000 _- 1 500
:I'. 2000 :— -: 250
U LILLLLILLLLlLLLL L l L L L L i L L L L l L L L L 1 LL: 0
\ 20 40 so so 100 150 200 250
Cf)
E—u 500
g .
O 300 .. .. g
C.) 5 g 3 ‘3’.
200 a a; .L § 8
n H
i a L,
100 3'
L l L L L L l L L L l L L L l L L L L l L L L L
300 350 400 450 500 550

CHANNEL

Figure V.3.5 Same as in Figure Figure V.3.1 with Argon (Ar).

v-1A7

120 (40Ar, 701), E/A=8 MeV

 

600'-

37:534

1' V

400

1,

511
38 638
37:726
38 755

- 36:788

37:90?

2001-

 

 

100 150 200 250
125.

100 1'

 

75 L i = 1'

COUNTS/CHANNEL

50L

38:1165
36:1730
35:1783

25 _

 

o J A A l a L A I l L n 1 1 l L 1 1 A I

 

 

300 350 400 450

CHANNEL

Figure V.3.6 Same as in Figure Figure V.3.1 with Chlorine (Cl).

COUNTS/CHANNEL

Figure V.3.7

12C

V-1A8

(“Ar 78), E/A=8

MeV

 

 

 

 

 

 

2
200
i :0 3 m ... :0
"l' ‘ N C 8 o O 0
F u 3 2
150' j I 8 g 8 " a: E
[ I I: 3 {'3 3
' 1 ML! ' I 'NL 1. f [
100:- . '1' : '_'[ [[7 J E [ 1
511 [i " ‘ [
50 -
0 ' 1 i L 1 1 L 1
C 100 150 200 250 300
IOOE- b
' 3
: [ 1 “’
I W [‘ [1L1 “ 1[ [v J :3
60 3 ‘ 1 [ 1‘ 1 [ 1 [ [[ I
: a ; i’
: 3 ‘
4O 7 t [g
: 3 "'
20E- 8
0 : L l L L L L I L L L . 1 L L L LL: L
350 400 450 500 550

CHANNEL

Same as in Figure Figure V.3.1 with Sulfur (S).

V-1’49

 

r V l r V V V I I' V V V l’ V T I

15000:- 12C (40Ar’ 7K)

 

 

 

 

‘

 

 

% E/A=8 MeV
M
CD 10000 - -
\ 1
U)
E"
Z
:3
O 5000 -
U .

0

0

Figure V.3.8 Doppler-shift corrected Y-ray energy spectra
coincidence with Potassium (K). a) At E/A=8 MeV.

 

(NaI) in

V-150

 

 

 

 

 

 

 

 

C 12 40
1000 - C ( A1", 7K) -
[E , E / A: 10 MeV L
M 800 - -
CD
\ 600:- Q
m ’ ’
B p
g 400 - -
O
o _ .
200 ~ -—
0 b . j . . I . . . i l L . i L l . . J A I
0 500 1000 1500 2000 »
E7 (KeV)

Figure V.3.8 (cont'd.) b) At E/A=10 MeV.

V-151

 

 

 

 

 

 

 

 

400 ' .1
' 1 12C (“An 7K)
3 ' E /A= 12 MeV
M 300 ' -
co 1
\ h ‘
m 200 "' i -
E—a .
Z
:9
O b L
U 100 _ -
00 L ‘ A A560 ‘ j + ‘10230‘ L L .1580. I A éOOO
E7 (KeV)

Figure V.3.8 (cont'd.) c) At E/A=12 MeV.

V-152

 

 

 

 

 

Table V.3.1 Relative gamma-ray intensities at E/Az8 MeV. a) For “5T1.

EY Decay B.R. N1 err. IY

(KeV) (1) (1) observed‘ CASC.2
15‘ 13’

585 3.60(-§')*3.02(-§ ) 82 45:20 0.322 1ui6 15
15‘ 11‘

15M? 3.02(—§-)+1.N7(-§-) 80 24:12 0.128 1919 17

1M69 1.N7(l%-)+ O(% ) 100 25:10 0.135 19:7 19

‘ Total number of gamma rays emitted during the entire runs through Mn

angle (unit: 1000 counts).

2 Predictions by the CASCADE code [P077] (normalized to EY:1469 KeV).

 

 

 

 

 

Table V.3.1 (cont'd.) b) For “°Ti.

EY Decay B.R. NY Eff. IY

(KeV) (1) (1) observed‘ CASC.2
13u5 6.2u(10*)»u.90(8*) 100 25:11 0.1u7 17:8 16
1289 3.30(6*) +2.01(u*) 100 58:29 0.159 38:16 28
1121 2.01(u*) +0.89(2+) 100 57:15 0.176 33:8 33
889 0.89(2*) » 0(0‘) 100 68:29 0.217 31:13 35
‘,2 Same as in Part a) except for a normalization to E :1121 Kev.

Y

V-153

Table V.3.2 Relative gamma-ray intensities at E/A:8 MeV.

a) For ““Sc.

 

 

 

I

 

 

 

Y Decay B.R. Y Eff. Y

(KeV) (1) (1) observed‘ Efl§9:2
5A6’ H.111 ? ):3.57(11*) 100 85:23 0.396 25:7

1083 3.98( 7 )+3.57(11*) 100 92:25 0.180 19:5

895 3.57(11*)+2.67(9‘) 100 139:45 0.216 57:21 51
1709 2.67(9+) +0.97(7+) 100 72:26 0.117 62:22 59
697 0.97(7+) +0.27(6*) 100 175:27 0.270 65:10 65
350* 0.35(u‘) » 0(2‘) 100 101:50 0.573 18:9 1

 

‘,2 Same as in Table V.3.1 except for a normalization to EY:697 KeV.

3

a.

11/2(O.35 MeV):3.1 ns

Uncertain spin assignment (no predicted value is given).

 

 

 

 

Table V.3.2 (cont'd.) b) For “580.
EY Decay B.R. NY err. IY
(KeV) (1) (7) observed‘ 01130.2
19' 15'
1586 3.69(—§-)+2.111—§ ) 100 52:20 0.125 50:17 59
870 2.1111; +1.2uclg ) 100 182:61 0.221 87:28 87
1237 1.2u(1%-)+ 0(%-) 100 203:30 0.160 127:19 95

 

 

 

‘,2 Same as in Table V.3.1 except for a normalization to EY:87O Kev.

V-15N

Table V.3.3 Relative gamma-ray intensities at E/A:8 MeV. a) For “ZCa.

 

EY Decay B R NY Eff. IY

(KeV) (1) (1) observed‘ CASC.2 ther.

 

 

382 7.75(11')+7.37(10‘) 100 867:200 0.518 167:39 310 87

815 7.37(10‘)»6.55(9’) 100
+810 6.55(9') :5.79(7') 72 2338:130 0.235 995:55 960 810
195 6.55(9‘) +6.91(8’) 28 1697:115 0.997 179:12 179 179
916 6.91(8’) +5.99(6’) 72
+909 9.10(5') +3.19(6‘) 67 1700:390 0.211 806:185 907 1180
1699 5.7917') ~9.10(5’) 59 585:280 0.121 983:231 279 399

939“ 3.19(6+) +2.75(9*1 100 2785:300 0.991 632:68 595 3610
1227 2.75(9+) +1.52(2*) 99 2359:350 0.161 1965:217 710 5530

1529 1.52(2*) + 0(0‘) 100 2090:185 0.130 1608:192 716 8710

1962 9.72(6+) ~3.25(9*) 95 510:210 0.135 378:156 18 362

1729 3.25(9*) +1.52(2*) 55 577:290 0.115 502:209 13 600

 

‘,2 Same as in Table V.3.1 except for a normalization to E

Y=1L15 KeV.
3 Predictions of thermal distribution with KT:2.76 MeV (normalized to
EY:195 KeV).

71/2(3.19 MeV):5.N ns.

V-155

Table V.3.3 (cont'd.) b) For “‘Ca.

 

 

 

 

 

 

EY Decay B.R. NY Eff. IY
(KeV) ‘ (1) (1) observed‘ CASC.2
776 5.93113- )+5.16(-]% 1 100
17" 15'
+761 5.16(*§ )+H.39(—§ ) 64 “851115 0.247 196:“? 6“

1076 2.75133 )»1.68(-%) 100 816:130 0.183 996:71 996

1678 1.681% 1» 017

373 0.371% ) + 01

100 963:990 0.118 7311295 692

) 100 227:100 0.532 ”3:19 123

 

‘,2 Same as in Table V.3.1 except for a normalization to E

Y

21076 KeV.

Table V.3.“ Relative gamma-ray intensities at E/Az8 MeV.

V-156

a) For “°K.

 

 

 

 

7 Decay B.R. Y
(KeV) (1)

1350 6.23(10’)»9.88<9+) 100 270:120
510 9.88(9*) +9.37(8*) 36 359:80
16513 2.59(7+) +0.89(5') 89 392:160
892 0.8915’) ~ 019') 100 1699:220

Eff.

(%)

0.176
0.372
0.120

0.216

I

 

Y
observed‘ CASC.2
185:82 90
95:21 39
2852133 321
787:102 787

 

‘,2 Same as in Table V.3.1 except for a normalization to EY=892 KeV.

3

‘1/2

(2.5“ MeV):1.1 ns

V-157

 

 

 

 

 

 

Table V.3.“ (cont'd.) b) For “‘K.
EY Decay B.R. NY Eff. IY
(KeV) (7) (1) observed‘ CASC.2
13+ 11+
296 2.77(—§ )~2.53(—§ ) 100 3503:155 0.838 “18:19 611
11+ 7+
851 2.53(-§-)+1.68(§ ) 100 1215:180 0.225 590:80 719
7+ 3+
1677 1.68(§ ) + 0(5 ) 100 9281135 0.118 7863115 786
709 9.991% 192811-31 100 1918:90 0.266 533:39 960
- +
1502 9.281131 12.7711; ) 20
+1515 9.28113- )+2.76(l-;-) 80 856:190 0.131 653:195 593
1967 2.7601;- 14.29%) 100 1067:180 0.135 790:133 535
3 1‘ 3"
1299 1.29(2 ) + 0(2 ) 100
',2 Same as in Table V.3.1 except for a normalization to E :1677 KeV.

3

T1/2

(1.29 KeV):7.2 ns.

Y

Table V.3.9 (cont'd.)

c) For “2K.

V-158

 

 

 

 

I

 

 

 

Y Decay B.R. Y Eff. Y
(KeV) (1) (1) observed‘ §fl§9:2
1093 9.60(9) +3.56(8) 100 115150 0.188 198:86 198
1612 3.56(8) +1.95(7*1 100 537:225 0.123 937:182 211
572 1.95(7+) +1.38(6+) 100 1123:95 0.329 391:29 260
678’ 1.38(6*) +0.70(5’) 90 760:165 0.278 273:60 300
990 0.70(5') +0.26(9‘) 96 1539:290 0.990 399:55 399
151 0.26(9‘) +0.11(3‘) 100 2556:190 0.919 278:21 372
107 0.11(3') : 0(2') 100 3191:380 0.970 329:39 902
‘,2 Same as in Table V.3.1 except for a normalization to E :990 KeV.

3

‘1/2

(1.38 KeV):1.1 ns.

Y

V-159

Table V.3.5 Relative gamma-ray intensities at E/A:8 MeV.

a) For ‘°Ar.

 

I

 

Y Decay B.R. Y Eff. Y
(KeV) (1) (7) observed‘ CASC.2 ther.’
1822 6.91(6*) +9.59(5’) 100 8321250 0.109 763:229 971 223
106 9.59(5') ~9.98(9‘) 90 8500:1600 0.970 876:165 1210 936
776 9.59(5’) +3.81(3") 10 5851105 0.295 239193 135 109
670 9.9819“) +3.81(3’) 100 36901190 0.281 1310170 1310 1310
1692 3.81(3') +2.17(2*) 100 20671265 0.121 17101220 1570 1855
2168 2.17(2*) + 0(0*) 100 5201160 0.0321 1630:500 1760 2701

 

 

 

 

‘,2 Same as in Table V.3.1 except for a normalization to EY=670 KeV.

3 Predictions of thermal distribution with xT=2.76 MeV (normalized to

EY

:670 KeV).

“ Limited detection efficiency.

 

 

 

 

 

 

Table V.3.5 (cont'd.) b) For 39Ar.
Ev Decay B.R. N7 Eff. 17
(KeV) (1) (1) observed‘ CASC.2
17+ 15+
992 5.59(-§ )+9.59(—§ ) 100 7361155 0.197 379179 569
15* 13*
551 9.59(-§-)+3.99(-§ ) 100 19961280 0.393 582182 699
13* 11'
1391 3.99(—§ )+2.65(-§-) 100 12711215 0.197 8651196 865
‘,2 Same as in Table V.3.1 except for a normalization to E =1391 KeV.

Y

V-160

Table V.3.6 Relative gamma-ray intensities at E/Az8 MeV. a) For 3"Cl.

 

 

 

 

 

E:Y Decay B.R. NY Eff. IY
(KeV) (1) (1) observed‘ ther.2
292 2.8116‘) +2.5215') 39 988151 0.701 70:7 28

17303 2.52(5*) ~0.79(3*) 96 250150 0.115 217193 173
788 0.79(3+) + 0(2*) 100 8701220 0.291 361191 361

1165 1.17(1*) + 0(2*) 100 198160 0.170 87:35 151

 

‘ Total number of gamma rays emitted during the entire runs through 99
angle (unit: 1000 counts).

2 Predictions of thermal distribution with KT:2.76 MeV (normalized to
EY:788 KeV).

(2.52 MeV):1.6 ns

3

‘1/2

Table V.3.6 (cont'd.) b) For “Cl.

 

E7 Decay B.R. N7 Eff. 11

(KeV) (1) (1) observed‘ CASC.2

 

 

726 5.2711; )+9.55(1%-) 100 270190 0.260 109115 288
539 9.55(l% )+9.01(% ) 100 12901260 0.359 350173 390

907 9.011% ) +3.10(% 1 69 613176 0.213 288136 288

 

‘,2 Same as in Table V.3.1 except for a normalization to EY=907 KeV.

V-161

Table V.3.7 Relative gamma-ray intensities at E/A:8 MeV. a) For 33S.

 

 

 

 

 

 

 

E1 Decay B.R. NY err. IY

(KeV) (1) (1) observed‘ ther.2
5* 3*

1966 1.97(§ ) 1 0(5 ) 100 270:60 0.101 267159 210

891 0.89(% ) + 0(% ) 100 213:50 0.228 93:22 93

 

‘ Total number of gamma rays emitted during the entire runs through 9n
angle (unit: 1000 counts).

2 Predictions of thermal distribution with KT:2.76 MeV (normalized to
EY:891 KeV).

Table V.3.7 (cont'd.) b) For 3“S.

 

EY Decay B.R. NY Eff. IY

(KeV) (1) (1) observed‘ ther.2

 

 

 

 

1001 5.69(5') +9.69(9*) 52 375172 0.195 192137 136
1066 5.69(5') +9.62(3’) 98 300159 0.189 163129 126
1320 9.62(3‘) +3.30(2*) 76 376196 0.150 251131 252
1176 3.30(2*) +2.13(2*) 56 213198 0.168 127129 127

2127 2.13(2*) + 0(0*) 100 377180 0.0973 8021170 1390

 

I 2

, Same as in Part a) except for a normalization to E :1176 KeV.

Y
3 Limited detection efficiency.

V-162

information for these nuclei, and also the calculation again predicts a
little larger populations at low-lying states, a calculation of the
Boltzmann thermal distribution shows only minor disagreement with the

observed data.

The comparable magnitude of the observed cross sections for Si and
P, as well as S and Cl, represent a major disagreement with the mass
spectra calculated by CASCADE code. As shown in Ch. 111, although it is
understood that the production of complex fragments with masses lighter
than half the compound nucleus is mainly due to the binary-decay process
of the composite system [Ch86a, M085, 8083], the origin of heavy
fragments (masses between the symmetric-fission product and the
projectile nucleus, e.g., Si, P, S, C1) is somewhat ambiguous; they
could be the binary-decay reaction partners of the complex fragments or
residual fragments of the composite system in the incomplete fusion
rather than in the complete fusion. Perhaps both processes are
responsible for the production of these fragments [M185]. This is
supported by the large yields of these fragments (Si, P, S, Cl, etc.) in
comparison with those for the complex fragments (Li, Be, 8, etc.). If
the binary-decay process was the main channel to populate these less
heavy residual fragments, the yields for these fragments should have
been comparable to those for the complex fragments. Massive cluster
transfer reactions with distinct Q-values and high, but less than ch,
angular momenta in the entrance channel have been introduced by
Morgenstern et al. [M086b] in order to obtain a new insight into the
reaction mechanism of incomplete-fusion events. However, without much

detailed knowledge of the incomplete-fusion mechanism, for example,

V-163

break-up of the target nucleus or the projectile nucleus, any attempt to
estimate the contribution from the incomplete-fusion process may not be
plausible. In Ch. 111, the average velocity for the heavy residual
fragments at a small angle (026° in Ref. M089b, 0=2.5° in Ref. M086b,
and 0:11° in the present experiment) seem to differ from one to another,
and this complicates the determination of the average momentum transfer.

Most gamma-ray peaks observed in coincidence with heavy residual
fragments turned out to belong to the transitions between high-spin
states, especially along the yrast-lines, which agrees with the basic
assumption of the statistical model. However the transitions from the
lower-spin states to the higher-spin states become observable as the
mass of the heavy fragments decreases. Predictions by the CASCADE code
[P1177] seem to agree roughly with the experimental data for the
population distribution of the high-spin states in isotopes of Ti and
So. Disagreement arises for some isotopes with Z < 21. In this less
heavy residual fragment region, the statistical model [P077] predicts,
in general, larger populations for higher—lying states or smaller ones
for lower-lying states. A thermal calculation, which is based on the
assumption of the Boltzmann distribution with KT=2.76 MeV, which is
predicted for E/Az8 MeV in the Fermi gas model, generally predicts the
opposite way; smaller populations for high-lying states or larger ones
for lower-lying states. Uncertainties in the level information do not
seem to explain the discrepancy for the latter case. However, the rough
agreement of the data with the thermal calculation for sulfur isotopes
may imply that the binary-decay process becomes more important in the
fragment forming channel as the mass gets lighter in this heavy residual

fragment region. The surprising result for 3aAr, which shows a rough

V-169

agreement between the CASCADE code prediction and the observed data, may
be interpreted to mean that the compound-nucleus decay dominates in the
production of fragments of this nucleus. This may be also supported tn!
the larger gamma-ray intensities for 3“Ar than for 39Ar, which is
consistent with the CASCADE code calculation.

In conclusion, the CASCADE statistical model calculation predicts
the population distributions of the nuclear states in the heavy residual
fragments with masses close to the maximum mass in the reaction. This
indicates that the statistical emission of the very light particles from
the complete-fusion product (compound nucleus) is a dominant process in
the production of those heavier residual fragments. However neither the
CASCADE code alone nor the Boltzmann thermal distribution with the Fermi
gas model temperature alone shows major agreement with the data fkn'
fragments of Z<21. Perhaps the incomplete-fusion process may contribute
significantly to the production of these less heavy residual fragments
[Mi85]. Alternatively, as no attempt has ever been made before to apply
the CASCADE code to predict the population distributions of nuclear
states in the heavy residual fragments, one may suspect the credibility
of the predictions for the population distributions of nuclear states by
the model. Nonetheless, an indication of the resemblance of the
population distributions among the low-lying states in the less heavy
residual fragments to the Boltzmann thermal distribution and a rough
agreement between the data and thermal calculation for sulfku~ isotopes
may tn; taken to imply that the binary-decay process of compound nucleus
also plays an appreciable role in the production of the heavy residual

fragments, and possibly a major role as the mass gets lighter.

CHAPTER VI: SUMMARY AND CONCLUSIONS

In continuation of a study of the statistical equilibrium in the
nuclear system [M086a], the reaction of ”Ar + ”C at E/A=8, 10, and 12
MeV was studied. Gamma-ray energy spectra were obtained for ganIna-rays
in coincidence with complex fragments and heavy residual fragments.
Particle singles inclusive spectra for the entire mass region (332522)
were also obtained owing to the excellent particle identification of the
silicon surface barrier particle telescopes. The use of the reverse
kinematics in the present experiment enabled the detection of the heavy
residual fragments. Population distributions of nuclear states in
complex fragments up to the symetric-fission limit and also those in
heavy residual fragments are investigated for the first time by the
measurement of the gamma—ray intensities.

Diagrams of the observed peak velocities for complex fragments
indicate the existence of a Coulomb velocity which is determined mainly
by the Coulomb repulsion energy in the binary decay process. The rough
coincidence between the center of the Coulomb velocities and the origin
of center-of—mass frame is taken as evidence that the complex fragments
are produced mainly from the compound nuclei via binary-decay processes.
A rough agreement between the median velocity of the backward-scattering
and forward-scattering peaks and the calculated value of VCMcoselab
enhances the characterization of compound-nucleus emission for complex

fragments. No major differences in the velocity diagrams or the

VI-165

Vl-166
comparison of median velocities are observed between different beam
energies.

Analysis of the simultaneous events for complex fragments in the
particle singles runs provides another dimension in a study of the
origin of these fragments. These events belong mostly to either between
telescope-1 and 9 or between telescope-2 and 3, which define two
scattering planes that intersect along the beam line. Very few
simultaneous events of complex fragments with large values of Z,+Z2 were
observed in the combinations of telescopes which define planes out of
the beam line. This indicates that the moving source of the complex
fragments must proceed in the beam direction. For the events with
smaller Z,+Z2, comparatively large contribution from the "out-of-plane"
combinations is observed, which may be due to the incomplete fusion or
continuous light particle emission after binary decay from the compound
nucleus; in both cases, the simultaneous events are not necessarily
confined to the "in-plane" combinations. A large number of events with
total charge (2:29) were observed at E/A=8 MeV for intermediate
fragments (Z>6), while few were observed at E/A=10 and 12 MeV. The
estimated average values of Z,+Z2 (about 23, 22, and 21 at E/A=8, 10,
and 12 MeV, respectively) are roughly consistent with the prediction
basing on the complete-fusion reaction.

The shift in the centroid velocity of heavy residual fragments away
from vCMcoselab is usually considered to be due to incomplete fusion in
the entrance channel [H187, M089b]. At 01ab=11°, the measured centroid
velocities for various fragments deviate from the predicted values. An
obvious trend is that, as the mass increases, the centroid velocity

decreases with respect to the predicted velocity of v coselab, which

CM

V1-167
indicates a tendency of the projectile break-up in the incomplete
fusion. This result disagrees with the abrasion model [Ch87a] and also
vdth the resulUspwesented in Ref. M089b, in which a tendency of the
target break-up in the reverse kinematics is exhibited. Hopefully,
further measurements of the cross sections of evaporation residues with
a wider mass range at various angles will help to solve this puzzle.

As an alternative to the moving source fits [We82, Ja83] for the
complex fragments, the kinetic energy spectra in the center-of-mass
frame were fitted by a Maxwell-Boltzmann function in order to check the
internal consistency of the slope parameters between complex fragments.
'Hmzrangecfl‘values was 2.7MeV-3.7Mev at E/A:8MeV, 3.9MeV-9.2MeV at
E/A:10MeV, and 3.5MeV-9.5Mev at E/A:12MeV, which shows the higher slope
parameter for the higher beam energy. A general trend that the slope
parameter decreases as the mass of the complex fragments gets heavier at
the same beam energy, which implies the lower temperatures for the
heavier complex fragments, are understood by the time evolution of the
temperature in a hot—equilibrated nuclear system [8086]. Nevert1ualess,
the slope parameters are very comparable to the predicted temperatures
by the Fermi Gas model, which are 2.8, 3.1, and 3.5 MeV at E/A=8, 10, 12
MeV, respectively, after taking the rotational energy into account. The
Coulomb shift parameter from the fitting is in a rough agreement with
the calculated Coulomb barrier potential for each isotope.

The relative population distribution of nuclear states among the
bound states were studied by the measurement of the gamma-ray
intensities in coincidence with the complex fragments. The deduced
temperatures, which reflect the relative populations of nuclear states

under the assumption of a simple Boltzmann distribution, are shown for a

Vl-168

summary in Figure VI.1.1 for the entire complex fragment region. For
‘Li, 7Be, and “’13, the deduced temperatures show a good agreement with
the pnwuiicted temperatures under the statistical equilibrium and also
with the slope parameters up to E/A:10 MeV. Comparison cfl‘tniis result
with a earlier study by Morrissey et al. [M086a] shows that these
fragments are produced from the equilibrated compound system, however a
correction must be made in the predicted temperatures in the Fermi gas
model by the subtraction of the rotational energy from the maximum
possible excitation energy in the full-momentum transfer reaction. At
E/A:12 MeV, while the temperature from ‘°B roughly agrees with that
predicted, those from 7Li and 7Be are significantly lower than
predicted. This is consistent in part with the result in Ref. Mo86a, in
which Morrissey et al. observed low temperatures from population
distributions at E/A=12 MeV and higher beam energies, however in the
present data t1u2.light fragments (7Li, 7Be, and ‘°B) did not give the
same temperature at E/A:12 MeV. This discrepancy is understood as to be
due to the effect of preferential feeding from higher-A nuclear systems
on the population distributions of these fragments. In the
determinatitn1<3f the 7Li gamma-fraction, contamination of the primary
population of 8Be ground state to the 7Li singles inclusive spectra has
been taken into account by means of a statistical theory [T088, Ha87]
and a Monte-Carlo simulation [8186], and it has been estimated to be 10%
at E/Az8 MeV, 9% at E/A:10 MeV, and negligible at E/A212 MeV.

This study has been extended more broadly in the present experiment
by the observation of the relative population of nuclear states in the
intermediate fragments (A>12). Temperatures extracted from the gamma-—

ray intensities in coincidence with H'N, "’0, “‘0, ”F, ”Ne, 2‘Ne,

VI-169
22Ne, and 23Na show a fluctuation ranging from 0.2 MeV to infinity. No
significant difference is observed between different beam energies,
which implies that the fluctuation may be due to some other physical
effect; in this thesis, a qualitative investigation regarding the effect
of the preferential feeding to certain states from the higher-A nuclear
unbound states [Ha88, Ha87, M085a, M089a, St83] on the measured
temperature has been carried out. The quantum statistical model [Fi87,
St83] looks successful in explaining this. Especially, as shown in

Figure 17.9.9b, the low gamma-fraction predicted by the quantum

+ +

statistical model for ”0 [0.891(5- ) 1 0(3 )] agrees remarkably well
with the data, while the predicted gamma-fraction from the primary
distribution is much higher than the experimental result. Low
temperatures from 7Li and 7Be at E/A:12 MeV may also be due to the
preferential feedings to the ground states of these mirror nuclei.
However, the model appears to overestimate the preferential feedings to
certain states in certain nuclei. In conclusion, the observed relative
population distributions of nuclear states in the complex fragment
region indicate that these fragments are produced from the equilibrated
compound system, however the preferential feedings from the higher-A
nuclear systems may have to be taken into account in the determination
of the nuclear temperatures.

Finally, the observed relative population distributions of bound
states in the heavy residual fragments are compared with the CASCADE
code calculation [P077]. The predicted yrast-line dominance of the
gamma-ray transitions agrees roughly with the data for the nuclei close

to the compound nucleus, which indicates that those fragments are formed

VI-170

from the compound nuclei in the full-momentum transfer reactions through
the statistical emission of the very light particles. The enhancement
of the states inside the yrast line and also of the low—lying states are
indicated only for nuclei far lighter than the compound nucleus. One
does not see any radical change between any neighboring isotopes,
however, one does see a notable trend of changing from the yrast-line
dominant population distributions to the Boltzmann distributions. The
Boltzmann distribution could be accidentally just a combination of the
population distributions from the compound nuclei in the complete fusion
and from the composite systems in the incomplete fusion with various
momentum transfers [M086b]. No further and more specific conclusions
regarding the production of the heavy residual fragments, for instance,
the fraction of the incomplete-fusion reaction with a certain type of
cluster transfer, the fraction of fission products, and the overall
contribution from the complete—fusion process, have been drawn in the
present measurement. It is strongly hoped in this thesis that this new
challenging measurement of the relative population distributions of
nuclear states in the heavy residual fragments by the detection of the
gamma-rays in coincidence with these fragments will help future
understanding in this field.

In conclusion, for the low energy reactions up to 12 MeV/nucleon in
the present experiment, the complex fragments are mainly produced from
the compound nuclei through a binary-decay process. The rough agreement
of the measured temperatures with those predicted after taking the
rotational energy and the preferential feedings into account indicates
that the compound system reaches thermal equilibrium before it starts

emitting complex fragments. Heavy residual fragments with masses near

VI-171
the cxnnpound nucleus are formed mainly from the compound nuclei via the
statistical emission of the light particles. However, as the mass of
the residual fragnmnts decreases away from the compound nucleus,
contributions from the decay of the composite systems in the incomplete-
fusicui reactions and also from the binary-decay process of the compound
rumdei may be more responsible for the production of the less heavy
residual fragments. In addition, it appears that the new nuclear
temperature measurement works roughly for fragments of A>10, too,
however in this region, the nuclear structure is too complicated for a
simple thermal model. Future improved measurements of this type will
help to understand the physics of statistical equilibrium of hot nuclear

matter and its decay modes.

VI-172

 

 

 

 

 

().1 7 l I l l l l l
A [
:> 10 4 [
<1)
3 1 .......................
\../ 1 + . 1+ '. ¢ .’
E + E/A=10 MeV
().1 l: l l l l l l I I l
10

 

 

+
A E/A=8 MeV
01 1 1 1 1 1 1 1 1 ,
7Li 7Be 10B 16N 1'70 180 19F 20NeZINezzNegaNa

Figure VI.1.1 Summary for the temperature measurements in the complex
fragment region. See Figures IV.3.3 and IV.9.3(a-c) for detail.

Aa79

Aj83

Aj89

Aj85

Aj86

Ba79
Be78

Be79

8175
B186

8089
8086

Br76

Bu55

Ch83

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